THE  UNIVERSITY 


OF  ILLINOIS 


« 


•  \ 


INTERNATIONAL 
LIBRARY  of  TECHNOLOGY 


A  SERIES  OF  TEXTBOOKS  FOR  PERSONS  ENGAGED  IN  THE  ENGINEERING 
.  PROFESSIONS  AND  TRADES  OR  FOR  THOSE  WHO  DESIRE 
INFORMATION  CONCERNING  THEM.  FULLY  ILLUSTRATED 
AND  CONTAINING  NUMEROUS  PRACTICAL 
EXAMPLES  AND  THEIR  SOLUTIONS 


BRIDGE  SPECIFICATIONS 
DESIGN  OF  PLATE  GIRDERS 
DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 
DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 
WOODEN  BRIDGES 
ROOF  TRUSSES 

BRIDGE  PIERS  AND  ABUTMENTS 
BRIDGE  DRAWING 


SCRANTON: 

INTERNATIONAL  TEXTBOOK  COMPANY 


97 


Copyright,  1908,  by  International  Textbook  Company. 


Entered  at  Stationers’  Hall,  London. 


Bridge  Specifications:  Copyright,  1907,  by  International  Textbook  Company. 
Entered  at  Stationers’  Hall,  London. 

Design  of  Plate  Girders:  Copyright,  1907,  by  International  Textbook  Company. 
Entered  at  Stationers’  Hall,  London. 

Design  of  a  Highway  Truss  Bridge:  Copyright,  1907,  by  International  Textbook 
Company.  Entered  at  Stationers’  Hall,  London. 

Design  of  a  Railroad  Truss  Bridge:  Copyright,  1907,  by  International  Textbook 
Company.  Entered  at  Stationers’  Hall,  London. 

Wooden  Bridges:  Copyright,  1907,  by  International  Textbook  Company.  Entered 
at  Stationers’  Hall,  London. 

Roof  Trusses:  Copyright,  1907,  by  International  Textbook  Company.  Entered 
at  Stationers’  Hall,  London. 

Bridge  Piers  and  Abutments:  Copyright,  1907,  by  International  Textbook  Com¬ 
pany.  Entered  at  Stationers’  Hall,  London. 

Bridge  Drawing:  Copyright,  1907,  by  International  Textbook  Company.  Entered 
at  Stationers’  Hall,  London. 


All  rights  reserved. 


Printed  in  the  United  States 


BURR  PRINTING  HOUSE 
FRANKFORT  AND  JACOB  STREETS 
NEW  YORK 


x 


A 


PREFACE 


The  International  Library  of  Technology  is  the  outgrowth 
of  a  large  and  increasing  demand  that  has  arisen  for  the 
Reference  Libraries  of  the  International  Correspondence 
Schools  on  the  part  of  those  who  are  not  students  of  the 
Schools.  As  the  volumes  composing  this  Library  are  all 
printed  from  the  same  plates  used  in  printing  the  Reference 
Libraries  above  mentioned,  a  few  words  are  necessary 
regarding  the  scope  and  purpose  of  the  instruction  imparted 
to  the  students  of — and  the  class  of  students  taught  by— 
these  Schools,  in  order  to  afford  a  clear  understanding  of 
their  salient  and  unique  features. 

The  only  requirement  for  admission  to  any  of  the  courses 
offered  by  the  International  Correspondence  Schools,  is  that 
the  applicant  shall  be  able  to  read  the  English  language  and 
to  write  it  sufficiently  well  to  make  his  written  answers  to 
the  questions  asked  him  intelligible.  Each  course  is  com¬ 
plete  in  itself,  and  no  textbooks  are  required  other  than 
those  prepared  by  the  Schools  for  the  particular  course 
selected.  The  students  themselves  are  from  every  class, 
trade,  and  profession  and  from  every  country;  they  are, 
almost  without  exception,  busily  engaged  in  some  vocation, 
and  can  spare  but  little  time  for  study,  and  that  usually 
outside  of  their  regular  working  hours.  The  information 
desired  is  such  as  can  be  immediately  applied  in  practice,  so 
that  the  student  may  be  enabled  to  exchange  his  present 
vocation  for  a  more  congenial  one,  or  to  rise  to  a  higher  level 
in  the  one  he  now  pursues.  Furthermore,  he  wishes  to 
obtain  a  good  working  knowledge  of  the  subjects  treated  in 
the  shortest  time  and  in  the  most  direct  manner  possible. 

iii 


342995 


IV 


PREFACE 


In  meeting  these  requirements,  we  have  produced  a  set  of 
books  that  in  many  respects,  and  particularly  in  the  general 
plan  followed,  are  absolutely  unique.  In  the  majority  of 
subjects  treated  the  knowledge  of  mathematics  required  is 
limited  to  the  simplest  principles  of  arithmetic  and  mensu¬ 
ration,  and  in  no  case  is  any  gre'ater  knowledge  of  mathe* 
matics  needed  than  the  simplest  elementary  principles  of 
algebra,  geometry,  and  trigonometry,  with  a  thorough, 
practical  acquaintance  with  the  use  of  the  logarithmic  table. 
To  effect  this  result,  derivations  of  rules  and  formulas  are 
omitted,  but  thorough  and  complete  instructions  are  given 
regarding  how,  when,  and  under  what  circumstances  any 
particular  rule,  formula,  or  process  should  be  applied;  and 
whenever  possible  one  or  more  examples,  such  as  would  be 
likely  to  arise  in  actual  practice — together  with  their  solu¬ 
tions — are  given  to  illustrate  and  explain  its  application. 

In  preparing  these  textbooks,  it  has  been  our  constant 
endeavor  to  view  the  matter  from  the  student’s  standpoint, 
and  to  try  and  anticipate  everything  that  would  cause  him 
trouble.  The  utmost  pains  have  been  taken  to  avoid  and 
correct  any  and  all  ambiguous  expressions — both  those  due 
to  faulty  rhetoric  and  those  due  to  insufficiency  of  statement 
or  explanation.  As  the  best  way  to  make  a  statement, 
explanation,  or  description  clear  is  to  give  a  picture  or  a 
diagram  in  connection  with  it,  illustrations  have  been  used 
almost  without  limit.  The  illustrations  have  in  all  cases 
been  adapted  to  the  requirements  of  the  text,  and  projec¬ 
tions  and  sections  or  outline,  partially  shaded,  or  full-shaded 
perspectives  have  been  used,  according  to  which  will  best 
produce  the  desired  results.  Half-tones  have  been  used 
rather  sparingly,  except  in  those  cases  where  the  general 
effect  is  desired  rather  than  the  actual  details. 

It  is  obvious  that  books  prepared  along  the  lines  men¬ 
tioned  must  not  only  be  clear  and  concise  beyond  anything 
heretofore  attempted,  but  they  must  also  possess  unequaled 
value  for  reference  purposes.  They  not  only  give  the  maxi¬ 
mum  of  information  in  a  minimum  space,  but  this  infor¬ 
mation  is  so  ingeniously  arranged  and  correlated,  and  the 


PREFACE 


v 


indexes  are  so  full  and  complete,  that  it  can  at  once  be 
made  available  to  the  reader.  The  numerous  examples  and 
explanatory  remarks,  together  with  the  absence  of  long 
demonstrations  and  abstruse  mathematical  calculations,  are 
of  great  assistance  in  helping  one  select  the  proper  for¬ 
mula,  method,  or  process  and  in  teaching  him  how  and 
when  it  should  be  used. 

This  volume  treats  of  the  design  and  construction  of 
bridges  and  roof  trusses.  As  an  introduction  to  the  subject, 
a  full  set  of  bridge  specifications  is  given.  These  specifica¬ 
tions  have  been  carefully  selected  and  compiled  from  those 
representing  the  best  modern  practice  among  bridge  engi¬ 
neers.  The  principles  of  design  are  fully  illustrated  by  the 
complete  design,  including  all  details,  of  several  plate-girder 
bridges,  a  highway  bridge,  and  a  railroad  bridge.  The  part 
on  wooden  bridges  is  a  very  simple  and  most  convenient 
presentation  of  a  subject  on  which  there  is  almost  no  easily 
accessible  literature.  The  design  and  construction  of  bridge 
piers  and  abutments,  which  forms  so  important  a  part  of 
bridge  engineering,  is  treated  with  the  thoroughness  that  its 
importance  demands.  Several  bridge-drawing  plates — com¬ 
plete  working  drawings — are  given  and  fully  described  in 
connection  with  the  design  work  dealt  with  in  the  text. 

The  method  of  numbering  the  pages,  cuts,  articles,  etc.  is 
such  that  each  subject  or  part,  when  the  subject  is  divided 
into  two  or  more  parts,  is  complete  in  itself;  hence,  in  order 
to  make  the  index  intelligible,  it  was  necessary  to  give  each 
subject  or  part  a  number.  This  number  is  placed  at  the  top 
of  each  page,  on  the  headline,  opposite  the  page  number; 
and  to  distinguish  it  from  the  page  number  it  is  preceded  by 
the  printer’s  section  mark  (§).  Consequently,  a  reference 
such  as  §  16,  page  26,  will  be  readily  found  by  looking  along 
the  inside  edges  of  the  headlines  until  §  16  is  found,  and 
then  through  §  16  until  page  26  is  found. 

International  Textbook  Company 


97 


CONTENTS 


Bridge  Specifications  Section 

Introduction . 74 

Plans  and  Proposals . 74 

Design  of  Railroad  Bridges . 74 

Design  of  Highway  and  Street-Railway 

Bridges . 74 

Construction  of  Steel  Bridges:  Materials  .  74 
Construction  of  Steel  Bridges:  Workman¬ 
ship  . . 74 

General  Remarks . 74 

Design  of  Plate  Girders 

Beams . 75 

Plate  Girders:  Section  Modulus . 75 

Plate  Girders:  Design  of  Flanges  ....  75 

Plate  Girders:  Design  of  Web  . 75 

Plate  Girders:  General  Design  .....  75 

Plate  Girders:  Splices . 75 

Plate  Girders:  Bearings . 75 


Design  of  an  I-Beam  Highway  Bridge  .  .  76 
Design  of  an  I-Beam  Railroad  Bridge  .  .  76 
Design  of  a  Plate-Girder  Railroad  Bridge  76 

Design  of  a  Highway  Truss  Bridge 

General  Features . 77 

Design  of  Floor  System:  Stringers  ...  77 
Design  of  Floor  System:  Intermediate 
Floorbeams  and  Brackets . 77 


Page 

1 

3 

5 

22 

42 

46 

54 


1 

3 
5 

10 

17 

19 

30 

1 

12 

19 

1 

4 

13 


in 


iv  CONTENTS 

Design  of  a  Highway  Truss  Bridge  Section  Page 
— Continued 

Design  of  Floor  System:  End  Floorbeam 

and  Bracket  .  .  .  ' .  77  22 

Stresses  in  Main  Members .  77  26 

Design  of  Main  Members .  77  34 

Design  of  Lateral  System .  77  42 

Floor  Connections . 78  1 

Splices . 78  14 

Design  of  Pins  and  Pin  Plates  . 78  16 

Bearings . 78  40 

Lateral  Connections .  78  43 

Bridge-Seat  Plan  .  78  45 

Design  of  a  Railroad  Truss  Bridge 

Data . 79  1 

Design  of  Floor  System:  Stringers  ...  79  3 

Design  of  Floor  System:  Intermediate 

Floorbeams . 79  10 

Design  of  Floor  System:  End  Struts  .  .  79  18 

Stresses  in  Main  Members .  79  21 

Design  of  Main  Members .  79  27 

Design  of  Lateral  System .  79  38  • 

Design  of  Chord  Splices .  79  48 

Design  of  Truss  Joints .  79  51 

Bearings .  79  61 

Bridge-Seat  Plan  . 79  64 

Wooden  Bridges 

Uses  and  Types  of  Wooden  Bridges  ...  80  1 

Materials  and  Working  Stresses  ....  80  4 

Kingpost  and  Kingrod  Trusses . 80  7 

Queenpost  and  Queenrod  Trusses  ....  80  14 

Howe  Truss .  80  24 

Towne  Lattice  Truss  .  . .  80  32 

Combination  Trusses  .  80  35 

Roof  Trusses 

Introduction  . 81  1 

Loads  and  Stresses  . 81  8 

V 


CONTENTS 


v 


Roof  Trusses — Continued  Section  Page 

First  Illustrative  Example . 81  14 

Second  Illustrative  Example . 81  21 

Third  Illustrative  Example . 81  30 

Design  of  Trusses  and  Lateral  Systems  .  81  41 

Design  of  Connections . 81  44 

Bridge  Piers  and  Abutments 

Definitions . 82  1 

Location  and  Estimates . 82  4 

Pier  Design:  Practical  Considerations  .  .  82  10 

Pier  Design:  Theoretical  Considerations  .  82  23 

Abutment  Design .  82  48 

Construction  .  82  62 

Bridge  Drawing 

Introduction . 83  1 

Drawing  Plates:  General  Considerations  .  83  8 

Drawing  Plate  107,  Title:  Highway-Bridge 

Details . 83  11 

Drawing  Plate  108,  Title:  Highway-Bridge 

Details . 83  19 

Drawing  Plate  109,  Title:  Highway-Bridge 

Details .  83  25 

Drawing  Plate  110,  Title:  Highway-Bridge 

Details .  83  31 

i 


t 


BRIDGE  SPECIFICATIONS 


INTRODUCTION 

1.  In  the  early  days  of  bridge  trusses,  when  wood,  being 
plentiful  and  cheap,  was  used  to  a  great  extent,  bridges 
were  invariably  built  without  plans,  and  in  a  great  many 
cases  without  previously  calculating  any  stresses  or  design¬ 
ing  any  members.  They  were  built  by  men  called  bridge 
carpenters ,  and  the  experience  of  the  foreman  or  superin¬ 
tendent  of  the  gang  usually  enabled  him  to  decide  on  the 
sizes  of  members  to  be  used.  As  the  loads  were  then  light 
and  timber  was  much  more  plentiful  than  it  is  now,  the 
errors  were  generally  on  the  side  of  safety;  that  is,  the 
bridges  were  made  more  than  strong  enough  for  the  loads. 

2.  When  wood  was  replaced  by  wrought  iron,  it  became 
necessary  to  manufacture  in  the  shops  most  of  the  members, 
and  designs  and  plans  were  made.  There  were  no  systematic 
scientific  methods  of  design,  however;  the  details,  instead 
of  being  proportioned  according  to  the  forces  they  were  to 
resist,  were  designed  and  arranged  as  seemed  most  conve¬ 
nient.  Many  bridges  at  that  time  were  designed  by  shop 
foremen  that  had  no  knowledge  of  stresses;  the  members 
were  laid  out  full  size  on  the  shop  floors,  and  made  so  as  to 
utilize  the  material  on  hand  in  the  stock  yard.  Very  few,  if 
any,  bridges  were  designed  to  allow  an  increase  in  the  loads 
they  were  to  carry  in  the  future. 

3.  Later,  engineers  began  to  realize  that  both  safety  and 
economy  required  that  bridges  should  be  designed  according 
to  scientific  principles  and  constructed  in  conformity  with 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

§74 


135-2 


2 


BRIDGE  SPECIFICATIONS 


74 


fixed  rules  derived  from  both  experience  and  theoretical 
investigations.  Such  rules,  when  assembled  together  for  the 
guidance  of  the  designer,  builder,  or  contractor,  are  called 
specifications.  Specifications  differed  greatly  at  first,  but 
after  a  short  time  they  began  to  approach  each  other,  and 
today  the  points  in  which  the  various  specifications  differ 
from  one  another  are  comparatively  few.  It  is  not  unlikely 
that  standard  specifications  for  the  construction  of  all 
bridges  of  the  same  type  will  be  adopted  in  the  near  future. 
The  introduction  of  such  uniform  system  will  greatly  facilitate 
bridge  design  and  construction. 

4.  When  the  earlier  bridges  were  finished,  the  plans,  if 
any,  that  had  been  used  in  the  design  and  construction  were 
either  destroyed  or  lost,  as  the  importance  of  saving  them 
for  future  reference  was  apparently  not  fully  realized.  As 
a  result,  there  are  at  the  present  time  many  bridges  in  use 
for  which  no  plans  can  be  found;  when  it  is  desired  to  know 
if  they  can  support  with  safety  heavier  loads  than  they  have 
been  carrying,  it  is  difficult  and  very  expensive  to  calculate 
their  strength,  for  it  is  first  necessary  to  measure  accurately 
the  span,  panel  length,  and  depth  of  girders,  and  trusses, 
the  cross-sections  of  stringers,  floorbeams,  girders,  and  truss 
members,  and  the  details  of  all  connections.  For  this  reason, 
it  has  become  the  custom  to  keep  on  file  detail  plans  of 
every  new  bridge;  these  plans  show  the  location  of  every 
rivet  and  the  size  of  every  piece  of  metal  in  the  structure, 
and  are  of  great  value  for  future  reference. 

5.  In  the  following  articles  are  given  bridge  specifica¬ 
tions  agreeing  with  the  best  practice  in  the  United  States  at 
the  present  time.  The  clauses  are  those  that  actual  practice 
has  shown  to  be  most  suitably  adapted  to  the  purposes  stated. 
Some  of  these  specifications  will  be  discussed  at  the  end  of 
this  Section;  others,  such  as  those  relating  to  plate  girders, 
will  be  given  in  the  Sections  on  design.  It  will  be  sufficient 
for  the  student  to  read  these  specifications  very  carefully, 
so  as  to  get  a  good  idea  of  their  contents;  it  is  not  neces¬ 
sary  to  memorize  them. 


§74 


BRIDGE  SPECIFICATIONS 


3  * 

The  bridges  in  the  following  Sections  will  be  designed 
according  to  these  specifications.  In  case  it  is  necessary  to 
design  bridges  according  to  other  specifications,  as  is  usually 
the  case  when  a  designer  works  for  a  bridge  or  railroad 
company,  it  will  simply  be  necessary  to  read  over  the  other 
specifications  and  design  the  work  accordingly. 


SPECIFICATIONS  FOR  THE  DESIGN  OF 

STEEL  BRIDGES 


PLANS  AND  PROPOSALS 

6.  Engineer  and  Contractor. — The  term  Engineer, 
where  used  in  these  specifications,  refers  to  the  Chief  or  Con¬ 
sulting  Engineer  in  charge  of  the  design  and  construction  of 
the  bridge,  and  to  his  duly  authorized  assistants  or  repre¬ 
sentatives.  The  term  Contractor  refers  to  the  bidder  to 
whom  the  contract  for  the  work  has  been  awarded,  and  to 
his  duly  authorized  representatives.  The  decision  of  the 
Engineer  shall  be  authoritative  in  all  cases  of  uncertainty. 

7.  Letter  of  Invitation. — A  copy  of  these  specifications 
will  be  furnished  each  bidder;  in  addition,  he  will  be  given 
a  letter  of  invitation  to  bid,  stating  the  general  descrip¬ 
tion  of  the  work  for  which  bids  are  desired  and  any  additional 

# 

facts  that  may  be  necessary.  In  case  the  requirements 
given  in  the  letter  of  invitation  conflict  in  any  way  with  those 
in  the  specifications,  those  in  the  letter  of  invitation  will  rule. 

8.  Bids. — Bids  shall  state  the  total  sum  for  which  the 
work,  as  described  in  the  letter  of  invitation,  will  be  done, 
the  estimated  weight,  and  price  per  pound,  of  each  class  of 
material,  and  the  amount  of  time  required  to  complete  the 
work.  They  shall  be  made  with  the  understanding  that 
the  Engineer  reserves  the  right  to  make  such  changes  in 
the  plans,  before  the  commencement  of  work,  as  may  be 
considered  advisable  by  him  to  render  the  bridge  a  satisfac¬ 
tory  piece  of  work.  The  increase  or  decrease  in  price  due 


4 


BRIDGE  SPECIFICATIONS 


§74 


to  such  change  shall  be  estimated  from  the  pound  price  of 
the  original  bid,  and  shall  be  added  to  or  deducted  from  the 
contract  price. 

9.  Extension  of  Time. — The  Contractor  shall  be  respon¬ 
sible  for  damages  on  account  of  delay  from  any  cause  during 
the  progress  of  the  work.  If  any  unforeseen  delay  shall 
arise,  it  will  entitle  him  to  an  extension  of  time,  to  be 
granted  in  writing  by  the  Engineer  at  the  time  of  the  delay. 

10.  Patent  Devices. — The  Contractor  shall  assume  all 
responsibility  for  the  use  of  patent  devices  in  any  part  of  the 
bridge,  or  in  connection  with  the  work  of  construction. 

11.  Subcontractors. — No  part  of  the  work  shall  be  sub¬ 
let,  nor  shall  the  contract  for  the  whole  or  any  part  of  the  work 
be  assigned  by  the  Contractor,  without  the  written  consent 
of  the  Engineer.  No  part  of  the  work  shall  be  done  in  a  shop 
hot  properly  equipped  with  modern  facilities.  These  specifi¬ 
cations  shall  be  binding  on  subcontractors  in  every  respect. 

12.  Plans  and.  Stress  Sheets. — As  a  rule,  the  Engineer 
will  provide  each  bidder  with  plans  and  stress  sheets,  show¬ 
ing  the  loads  assumed,  the  resulting  stresses,  the  proposed 
sizes  and  sectional  areas  of  the  members,  and  the  style  of 
the  details  and  connections,  as  well  as  lengths,  heights,  and 
clearances.  The  bidder  shall  verify  the  plans  before  he 
submits  his  bid,  and  he  alone  shall  be  responsible  for  any 
errors,  except  as  to  general  layout.  He  shall  return  the 
Engineer’s  plans  if  his  bid  is  not  accepted.  If  the  Engineer 
does  not  furnish  plans  and  stress  sheets  as  described,  the 
bidder  shall  furnish  them  with  his  bid,  if  requested  to  do  so 
by  the  Engineer. 

13.  Working  Drawings. — After  a  contract  has  been 
awarded  and  before  any  material  is  ordered  or  work  com¬ 
menced,  the  Contractor  shall  submit  to  the  Engineer  three 
complete  sets  of  working  drawings,  including  erection  dia¬ 
grams.  When  satisfactory,  one  set  of  such  drawings  and 
diagrams  will  be  approved  and  returned  to  the  Contractor, 
and  all  work  shall  be  done  in  accordance  with  them.  The 


74 


BRIDGE  SPECIFICATIONS 


5  * 

Contractor  alone  shall  be  responsible  for  the  correctness  of 
these  drawing's,  even  if  they  have  been  approved  by  the 
Engineer.  No  changes  shall  be  made  on  the  drawings  after 
they  have  been  approved,  unless  authorized  in  writing  by 
the  Engineer.  On  the  completion  of  the  work,  the  Con¬ 
tractor  shall  furnish  the  Engineer  one  complete  set  of  tra¬ 
cings  of  the  working  drawings,  which  will  be  permanently 
filed  in  the  office  of  the  Engineer.  The  Contractor  shall, 
when  required,  furnish  also  the  necessary  plans  for  design¬ 
ing  the  masonry. 

Drawings  shall  preferably  be  not  more  than  24  in.  X  36  in., 
with  details  drawn  to  a  scale  of  1  or  1  inch  to  1  foot. 


DESIGN  OF  RAILROAD  BRIDGES 


GENERAL  DIMENSIONS 

14.  Kinds  of  Bridges. — The  following  kinds  of  bridges 
shall  preferably  be  used: 

For  spans  less  than  25  feet  in  length,  rolled  beams. 

For  spans  from  25  to  100  feet  in  length,  plate  girders. 

For  spans  from  100  to  150  feet  in  length,  riveted  trusses. 

For  spans  over  150  feet  in  length,  pin-connected  trusses. 

If,  for  any  reason,  it  is  desired  to  depart  more  than  10  feet 
from  these  limits,  permission  in  writing  must  be  obtained 
from  the  Engineer. 

Deck  bridges  will  have  the  preference  wherever  the  con¬ 
ditions  permit  their  use. 

15.  Panel  Eengths  and  Depths. — The  depth  of  plate 
girders  shall  preferably  be  one-eighth,  and  in  no  case  less 
than  one-twelfth,  of  the  span.  The  depth  of  trusses  shall 
preferably  be  not  less  than  one-sixth  of  the  span.  Panel 
lengths  shall  preferably  be  from  10  to  25  feet,  and  in  truss 
bridges  shall  be  so  chosen  that  the  angle  between  diagonal 
web  members  and  the  lower  chord  shall  be  not  less  than  50°. 

16.  Spacing  of  Stringers  and  Deck  Girders. — * 
Stringers  shall  be  spaced  6  feet  6  inches  center  to  center. 


\ 


6 


BRIDGE  SPECIFICATIONS 


S74 


Deck  girders  less  than  70  feet  long  shall  be  spaced  6  feet 
6  inches  center  to  center;  deck  girders  over  70  feet  long 
shall  be  spaced  6  inches  farther  apart  for  each  10  feet  increase 

in  length.  In  bridges  on  curves,  the  center 
line  between  stringers,  and  between  deck 
girders,  shall  be  parallel  to  the  chord  of  the 
|  curve  between  abutments,  and  at  a  distance 
"b  from  it  equal  to  two -thirds  the  middle 
'•§  ordinate. 

17.  Half -Through  Bridges. — Half- 
through  truss  bridges  shall  be  avoided  when 
fig.i  possible.  Where  used, Ohe  flanges  and 

brackets  shall  not  come  closer  to  the  center  line  of  track  than 
shown  in  outline  in  Fig.  1. 

18.  Th  rough  Bridges.  —  In  through  bridges  on 
straight  track,  no  part  of  the  structure  shall  come  closer  to 
the  center  line  of  the  nearest  track  than 
shown  in  outline  in  Fig.  2.  In  bridges 
on  curves,  there  shall  be  provided  1  inch 
additional  clearance  on  each  side  of  the 
track  for  each  degree  of  curvature,  and 
2|  inches  additional  clearance  on  the 
inside  of  the  curve  for  each  inch  of 
superelevation  of  track. 

19.  Spacing  and  Gauge  of 
Tracks.  —  Tracks  shall  be  spaced 
13  feet  center  to  center,  unless  other¬ 
wise  specified.  The  gauge  of  track  is 
4  feet  8i  inches. 

20.  Spacing  of  Trusses. — The 

distance  center  to  center  of  trusses  shall 
preferably  be  not  less  than  one-twelfth 
the  span,  and  in  no  case  less  than  one- 
half  the  depth  of  trusses.  Fig.  2 

21.  Double-Track  Spans. —  Double-track  spans  shall 
preferably  have  only  two  trusses  or  girders.  Where,  on 


§74 


BRIDGE  SPECIFICATIONS 


7  * 


account  of  thin  floors,  three-truss  bridges  are  advisable,  the 
tracks  shall  be  spread  so  as  to  provide  the  proper  clearance 
between  the  trusses  for  each  track. 


LOADING 

22.  Loads. — Bridges  shall  be  designed  to  resist  properly 
the  stresses  caused  by  the  following  forces:  dead  load;  live , 
or  moving,  load ;  impaci  and  vibration;  centrifugal  force;  wind 
pressure;  and  the  longitudi?ial  force  due  to  suddenly  stopping 
trains. 

23.  Dead  Load. — The  dead  load  shall  consist  of  the 
estimated  weight  of  the  entire  structure.  The  weight  of 
ties,  guard  timbers,  and  rails  shall  be  taken  as  400  pounds 
per  linear  foot  of  track,  of  timber  as  4i  pounds  per  board 
foot,  and  of  ballast  as  120  pounds  per  cubic  foot.  In  truss 
bridges,  two-thirds  of  the  dead  load  shall,  in  general,  be 
assumed  as  applied  at  the  loaded  chord,  and  one-third  at  the 
unloaded  chord. 


24.  Live  Load. —  The  live  load  on  each  track  shall 
consist  of  two  engines  followed  by  a  uniform  load  of  5,000 
pounds  per  linear  foot,  as  represented  in  Fig.  3,  or  a  loading 


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having  the  same  spacing  of  wheels  and  derived  from  the 
former  by  multiplying  each  load  by  the  same  number. 


25.  Impact  and  Vibration. — To  provide  for  impact 
and  vibration,  an  amount  /  is  to  be  added  to  the  stress  or 
bending  moment  in  each  member,  as  given  in  the  following 
formulas,  in  which 

^  =  maximum  live-load  stress  or  bending  moment  in  the 
member; 

L  =  length,  in  feet,  of  single  track  that  must  be  loaded  in 
order  to  obtain  the  value  S. 


8 


BRIDGE  SPECIFICATIONS 


74 


For  counters,  hip  verticals,  subverticals,  short  diagonals, 
floor  members  and  connections,  and  members  subject  to 
reversal  of  stress, 

7=5 

For  all  other  members, 

T  _  300  s 

~  L  +  300 

26.  Centrifugal  Force. — In  bridges  on  curves,  the 
centrifugal  force  F  shall  be  found  from  the  formula 

F  =  l4,5  ~  -2-2 o  W 
100 

in  which  D  =  degree  of  curvature; 

W  —  live  load. 

Centrifugal  force  shall  be  assumed  to  act  6  feet  above  the 
rail. 

27.  Wind  Pressure. — Wind  pressure  shall  be  assumed 
as  300  pounds  per  linear  foot  on  a  train,  applied  7  feet  above 
the  top  of  the  rail,  and  30  pounds  per  square  foot  on  the 
exposed  area  of  one  girder  in  girder  bridges,  one  truss  in 
through  bridges,  or  two  trusses  in  deck  bridges,  together 
with  the  floor  in  truss  bridges.  When  50  pounds  per  square 
foot  on  twice  the  exposed  area  of  one  truss  and  the  exposed 
area  of  the  floor,  with  no  train  on  the  bridge,  produces 
greater  stresses  than  the  above,  the  greater  stresses  shall 
be  used. 

28.  Suddenly  Stopping  Trains. — The  longitudinal 
force  due  to  the  friction  between  the  rails  and  the  wheels 
of  suddenly  stopping  trains  shall  be  taken  as  one-fifth  of 
the  live  load  on  the  structure. 


DESIGN  OF  MEMBERS 

29.  Working  Stresses. — All  parts  shall  be  so  designed 
that  the  sum  of  the  maximum  .stresses  in  any  part  shall  not 
cause  the  intensity  of  stress  to  exceed  the  following  values 
in  pounds  per  square  inch: 

Tension  on  net  section,  16,000. 


§74 


BRIDGE  SPECIFICATIONS 


9  * 


Compression  on  gross  section, 

16,000 

r 

l  h - - - 

18,000  r2 

in  which  l  =  unsupported  length  of  member,  in  inches; 
r  =  least  radius  of  gyration,  in  inches. 

In  half-through  truss  bridges,  the  entire  length  of  the 
upper  chord  shall  be  considered  unsupported  laterally. 

Shear  on  net  section  of  web-plates, 

.  12,000 

i  +  -^_ 

3,000  e 

in  which  t  =  thickness  of  web,  in  inches; 

d  —  clear  distance,  in  inches,  between  stiffeners  or 
flange  angles,  whichever  is  the  smaller. 

The  intensity  of  the  shearing  stress  found  by  dividing  the 
total  vertical  shear  by  the  gross  area  of  cross-section  of  the 
web  shall  in  no  case  exceed  9,000. 

Shear  on  shop  rivefcs  and  pins,  11,000. 

Shear  on  field  rivets  and  turned  bolts,  9,000. 

Bending  on  pins,  22,000. 

Bending  on  rolled  sections  and  plate  girders: 

Tension,  16,000. 

Compression,  when  unsupported  length  l  of  compres¬ 
sion  flange  is  not  greater  than  twenty  times  the 
width  w,  16,000. 

Compression,  when  /  is  greater  than  20  w, 

20,000  -  200  — 

W 

Bearing  on  shop  rivets  and  pins,  22,000. 

Bearing  on  field  rivets,  turned  bolts,  and  ends  of  stiffeners, 
18,000. 

Bearing  on  masonry: 

Sandstone  and  limestone,  300. 

Cement  concrete,  400. 

Granite,  500. 

Bearing  on  rollers  shall  not  exceed  600  D  pounds  per 
linear  inch  of  roller,  D  being  diameter  of  roller  in  inches. 


10 


BRIDGE  SPECIFICATIONS 


74 


30.  Data. — The  following  general  dimensions  shall  first 
be  calculated  or  assumed: 

Length  of  trusses,  center  to  center  of  end  pins  or  pedestals. 

Length  of  girders,  center  to  center  of  bearings. 

Length  of  floorbeams,  center  to  center  of  girders  or 
trusses. 

Length  of  stringers,  center  to  center  of  floorbeams. 

Depth  of  trusses  and  girders,  center  to  center  of  gravity 
of  chords  or  flanges. 

31.  Floor  Members. — Solid  floor  sections,  I  beams,  and 
channels  shall  be  designed  by  their  moments  of  inertia,  or 
section  moduli.  The  load  on  each  axle  shall  be  assumed  to 
be  distributed  over  a  length  of  3  feet  in  designing  solid  floor 
sections.  In  bridges  on  curves,  stringers  and  deck  girders 
shall  be  designed  for  the  increase  in  load  due  to  the 
eccentricity  of  the  track. 

32.  Compression  Members. — Pin  and  bolt  holes  shall 
be  deducted  from  the  gross  section  of  Compression  members. 

The  value  of  -  shall  preferably  be  from  40  to  60,  and  must 

r 

not  exceed  100  for  main  members,  nor  120  for  members  of 
lateral  systems.  Splices  in  compression  members  shall  have 
sufficient  rivets  to  fully  develop  the  stresses  in  the  members. 

33.  Tension  Members. — The  net  section  of  a  riveted 
tension  member  shall  be  determined  by  deducting  from  the 
gross  section  the  area  of  cross-section  of  the  greatest  num¬ 
ber  of  pin,  bolt,  or  rivet  holes  that  can  be  cut  by  a  plane  at 
right  angles  to  the  member.  In  addition,  for  rivets  i  inch 
in  diameter  and  larger,  there  shall  be  deducted  each  hole 
whose  center  lies  within  f  inch  of  the  cutting  plane,  and  a 
proportionate  part  of  each  hole  whose  center  lies  within 
2f  inches;  and  for  rivets  1  inch  in  diameter  and  smaller,  each 
hole  whose  center  lies  within  \  inch  of  the  cutting  plane,  and 
a  proportionate  part  of  each  hole  whose  center  lies  within 
2  inches.  Rivet  holes  shall  be  taken  i  inch  larger  in  diameter 
than  the  rivets. 


74 


BRIDGE  SPECIFICATIONS 


11 


34.  Reversal  of  Stress. — Members  subject  to  both 
tension  and  compression  shall  be  designed  to  resist  each 
stress  plus  eight-tenths  of  the  other  stress. 

35.  Combined  Stresses. — Members  subject  to  trans¬ 
verse  stresses  in  addition  to  the  direct  stresses  shall  be 
designed  for  both. 

36.  Bearing  Values  of  Rivets. — In  calculating  the 
bearing  value  of  a  rivet,  the  area  subjected  to  stress  shall 
be  taken  as  equal  to  the  product  of  the  thickness  of  the  plate 
and  the  diameter  of  the  rivet  before  driving,  that  is,  the 
nominal  diameter.  .  The  value  of  countersunk  rivets  shall 
not  be  counted. 


GENERAL  DETAILS 

37.  General  Requirements  for  Details  and  Con¬ 
nections. — Special  attention  shall  be  given  to  all  details 
and  connections;  they  shall  always  be  of  greater  strength 
than  the  body  of  the  member.  All  details  shall  be  accessible 
for  inspection,  cleaning,  and  painting.  Details  that  permit 
the  collection  of  water  shall  be  avoided  if  possible;  if  used, 
they  shall  be  provided  with  drainage  holes  or  filled  with 
cement  concrete. 

38.  Minimum  Thickness. — No  material  less  than 
f  inch  thick  shall  be  used  except  for  latticing  and  fillers. 

39.  Single  Angles. — Members,  or  sides  of  members, 
composed  of  single  angles  shall  have  both  legs  of  each 
angle  connected  at  the  ends,  or  only  75  per  cent,  of  the  sec¬ 
tion  shall  be  counted.  No  angle  shall  be  smaller  than 
3  in.  X  3  in.  X  t  in.,  nor  be  connected  by  less  than  four 
rivets,  except  for  unimportant  details. 

40.  Size  of  Rivets. — Rivets  shall  generally  be  i  inch 
and  !  inch  in  diameter.  The  diameter  of  the  rivet  shall  not 
be  greater  than  one-fourth  the  width  of  the  bar  or  angle 
through  which  the  rivet  passes,  except  for  unimportant 
details,  where  f-inch  rivets  may  be  used  in  3-inch  angles, 
and  f-inch  rivets  in  2i-inch  angles. 


12 


BRIDGE  SPECIFICATIONS 


§74 


41.  Spacing  of  Rivets. — Rivets  i  inch  in  diameter 
shall  be  spaced  not  more  than  6  nor  less  than  3  inches  center 
to  center,  and  placed  not  closer  than  If  inches  to  any  sheared 
edge  nor  closer  than  li  inches  to  any  rolled  edge — except  in 
special  cases  to  conform  to  standards,  where  they  may  be 
placed  not  closer  than  li  inches  to  a  rolled  edge.  Rivets 
I  inch  in  diameter  shall  be  spaced  not  more  than  6  nor  less 
than  2i  inches  center  to  center,  and  placed  not  closer  than 
li  inches  to  any  sheared  edge  nor  closer  than  li  inches  to 
any  rolled  edge — except  to  conform  to  standards,  where 
they  may  be  placed  not  closer  than  li  inches  to  a  rolled 
edge.  The  spacing  of  rivets  at  the  ends  of  compression 
members  shall  not  exceed  four  times  the  diameter  of  the 
rivets  for  a  distance  equal  to  the  width  of  the  member. 

42.  Grip  of  Rivets. — The  grip  of  rivets  shall  prefer¬ 
ably  not  exceed  five  times  the  diameter  of  the  rivet,  and 
shall  in  no  case  exceed  5  inches.  When  the  grip  is  greater 
than  4  inches,  the  calculated  number  of  rivets  shall  be 
increased  1  per  cent,  for  each  rt  inch  increase  in  grip. 

43.  Compression  Members. — In  compression  mem¬ 
bers,  the  material  shall  mostly  be  concentrated  at  the  sides. 
The  unsupported  widths  of  plates  shall  not  exceed  thirty 
times  their  thickness  for  web-plates,  nor  forty  times  their 
thickness  for  cover-plates  of  chords  and  end  posts.  No 
closed  sections  will  be  allowed. 

44.  Tie-Plates  and  Lattice  Bars. — The  open  sides 
of  all  built-up  members  shall  be  stiffened  by  means  of  tie- 
plates  and  lattice  bars.  The  length  of  tie-plates  shall  be 
not  less  than  li  times  the  width  of  the  member.  Double 
latticing  shall  preferably  make  an  angle  of  about  45°  with 
the  axis  of  the  member,  and  the  bars  shall  be  riveted  where 
they  cross  each  other.  Single  latticing  shall  preferably 
make  an  angle  of  about  60°  with  the  axis  of  the  member. 
Bars  in  single  latticing  shall  have  a  thickness  not  less  than 
one-fortieth,  and  in  double  latticing  not  less  than  one-sixtieth, 
of  the  length  of  the  bar.  Lattice  bars  shall  be  not  less  than 
2i  inches  wide  for  members  up  to  9  inches,  not  less  than 


74 


BRIDGE  SPECIFICATIONS 


13 


2  k  inches  for  members  from  9  to  15  inches,  and  not  less  than 

3  inches  for  members  more  than  15  inches  in  width  or  depth. 

45.  Expansion. — Provision  for  expansion  and  contrac¬ 
tion  due  to  changes  of  temperature  shall  be  made  at  the  rate 
of  1  inch  for  every  100  feet. 

46.  Camber. — All  trusses  shall  be  cambered  by  giving 
the  panels  of  the  top  chord  an  excess  of  length  in  the  pro¬ 
portion  of  i  inch  to  every  10  feet.  Plate  girders  shall  not 
be  cambered. 

47.  I  Beams. — In  short  deck  spans,  when  more  than 
one  I  beam  is  used  under  a  rail,  the  beams  shall  be  bolted 
together  with  cast-iron  separators  between  them,  and  con¬ 
nected  by  lateral  bracing  between  the  two  sets  of  beams. 


DETAILS  OF  FLOOR  SYSTEMS 

48.  Ties,  Guard  Timbers,  and  Rails. — Ties,  guard 
timbers,  rails,  wooden  floors,  and  ballast,  where  necessary, 
will  be  provided  and  put  in  place  by  the  railroad  company. 
Cross-ties  are  8  in.  X  8  in.,  10  feet  long,  framed  to  not  less 
than  7k  inches  over  bearings  for  stringers  and  girders  6  feet 
6  inches  center  to  center.  The  depth  of  the  tie  is  increased 
1  inch  for  each  6  inches  additional  width  of  girders.  Ties 
are  spaced  12  inches  center  to  center,  and  every  fourth  tie  is 
fastened  to  each  stringer  by  a  1-inch  bolt.  Guard  timbers 
are  8  inches  wide  and  6  inches  thick,  framed  to  4  inches  over 
ties,  and  spaced  4  feet  from  inner  edge  to  center  of  track. 
They  are  fastened  by  f-inch  bolts  to  the  ties  that  are  con¬ 
nected  to  the  stringers. 

49.  Floor  Members. — Floor  members  shall  be  designed 
with  special  reference  to  stiffness;  the  depth  of  stringers 
shall  be  not  less  than  one-eighth  of  the  panel  length,  and 
that  of  floorbeams  not  less  than  one-sixth  of  the  distance 
between  trusses  or  girders. 

50.  Floor  Connections. — Stringers  shall  be  at  right 
angles  to  the  floorbeams,  and  shall  be  riveted  to  the  floor- 
beam  webs.  If  possible,  they  shall  also  rest  on  shelf  angles 


14 


BRIDGE  SPECIFICATIONS 


74 


riveted  to  the  webs  of  the  floorbeams.  Floorbeams  shall 
preferably  be  at  right  angles  to  the  girders  or  trusses.  In 
half-through  plate-girder  bridges,  the  beams  shall  be  riveted 
to  the  webs  of  the  girders.  In  through  truss  bridges,  the 
beams  shall  be  riveted  to  the  vertical  posts,  or  to  the  web 
connection  plates;  if  there  are  no  vertical  posts,  diaphragms 
shall  be  riveted  in,  connecting  the  web  connection  plates  at 
the  ends  of  the  floorbeams.  In  deck  truss  bridges,  the 
beams  shall  either  be  riveted  to  the  trusses  as  in  through 
bridges,  or  rest  on  the  upper  chords. 

51.  Connection  Angles. — The  connection  angles  of 
stringers  to  floorbeams,  and  floorbeams  to  girders  and 
trusses,  shall  not  be  smaller  than  3i  in.  X  32  in.  X  i^s  in. 
The  fillers  under  connection  angles  shall  be  wider  than  the 
adjacent  leg  of  the  angle,  and  shall  have  two-thirds  as 
many  rivets  through  the  projecting  portion  as  through  the 
portion  under  the  angle. 

52.  Deck  Bridges. — In  deck  girder  bridges,  the  ties 
shall  rest  directly  on  the  top  flange.  In  deck  truss  bridges, 
the  ties  shall  not  rest  directly  on  the  top  chord  members; 
there  shall  always  be  a  floor  system  with  floorbeams  at  the 
panel  points. 

53.  End  Floorbeams. — All  bridges  with  floor  systems 
shall  preferably  be  provided  with  end  floorbeams  of  the  same 
cross-section  as  intermediate  floorbeams.  Where  this  is 
impossible,  the  end  stringers  shall  rest  on  the  masonry;  end 
struts,  of  nearly  the  same  depth  as  the  end  stringers,  shall 
be  riveted  to  them  and  to  the  girders  or  trusses. 

54.  Solid  Floors. — Solid  floors  shall  preferably  be  made 
of  a  plate  not  less  than  tg  inch  thick  riveted  to  the  tops  of 
longitudinal  I  beams  supported  by  floorbeams. 


DETAILS  OF  PLATE  GIRDERS 

55.  Stiffeners. — Webs  shall  have  stiffeners  over  bear¬ 
ing  points,  at  points  of  local  concentrated  loadings,  and  at 
intervals  not  greater  than  the  depth  of  the  girder  nor  more 


§74  . 


BRIDGE  SPECIFICATIONS 


15  * 


than  6  feet.  Near  the  ends,  the  spacing  of  stiffeners  shall 
be  one-third  to  one-half  the  depth.  They  shall  be  composed 
of  two  angles,  one  on  each  side  of  the  web,  and  shall  fit 
tight  between  the  horizontal  legs  of  the  flange  angles.  For 
girders  having  flange  angles  with  outstanding  or  horizontal 
legs  5  inches  in  width,  stiffeners  shall  be  not  less  than 
4  in.  X  3i  in.  X  t  in.;  with  outstanding  legs  6  inches  in 
width,  not  less  than  5  in.  X  3i  in.  X  f  in.;  and  with  outstand¬ 
ing  legs  8  inches  in  width,  not  less  than  6  in.  X  3i  in.  X  I  in. 
Rivets  in  stiffeners  shall  be  spaced  not  over  3i  inches  apart 
for  a  distance  of  14  inches  at  each  end,  and  not  over  6  inches 
apart  for  the  remaining  distance.  When  the  clear  vertical 
distance  between  flange  angles  is  less  than  fifty  times  the 
thickness  of  the  web,  stiffeners  may  be  omitted — except 
over  bearings,  where  they  shall  be  designed  to  resist  the 
reactions. 

56.  Web  Splices. — Web-plates  shall  be  spliced  by  one 
or  more  plates  on  each  side;  the  splice  plates  shall  have  a 
section  equal  to  at  least  three-fourths  that  of  the  web,  and  a 
pair  of  stiffeners  shall  be  placed  outside  the  plates.  There 
shall  be  not  less  than  two  rows  of  rivets  3i  inches  apart  on 
each  side  of  the  splice;  rivets  in  splice  plates  shall  be  spaced 
not  over  3i  inches  apart  for  a  distance  of  14  inches  at  top 
and  bottom,  and  not  over  4}  inches  between.  Web  splices 
shall  be  designed  for  the  same  resisting  moment  as  the 
web. 

57.  Flange  Rivets. — The  pitch  of  rivets  connecting  the 
flange  angles  to  the  web  at  any  point  shall  be  calculated  by 
the  formula 


in  which  p  —  pitch,  in  inches; 

K  =  smallest  value  of  the  rivet,  in  pounds; 
hr  =  vertical  distance,  in  inches,  between  centers 
of  rivet  lines  of  flanges; 

V  =  total  maximum  vertical  shear,  in  pounds,  at 
the  section. 


16 


BRIDGE  SPECIFICATIONS 


74 


When  the  ties  rest  on  the  top  flanges  of  deck  girders,  the 
pitch  of  rivets  in  the  top  flange  shall  be  90  per  cent,  of  the 
calculated  pitch.  The  rivets  connecting  flange  plates  to 
flange  angles  shall  have  the  same  spacing  as,  and  stagger 
with,  those  connecting  the  flange  angles  to  the  web.  The 
spacing  of  rivets  in  plate-girder  flanges  shall  in  no  case 
exceed  4i  inches. 

58.  Flanges. — Flanges  shall  be  designed  by  the  net  sec¬ 
tion  of  the  bottom  flange  and  by  the  gross  section  of  the  top 
flange.  One-eighth  of  the  web  shall  be  considered  as  part 
of  the  flange  section.  Girders  with  deep  webs  may  have 
flanges  composed  of  vertical  as  well  as  horizontal  flange 
plates  and  secondary  flange  angles. 

59.  Flange  Angles. — Flange  angles  shall  preferably  be 
of  large  sections;  in  general,  not  less  than  one-third  to  one- 
half  the  flange  section  shall  be  composed  of  angles. 

60.  Flange  Plates.  —  Flange  plates  shall  preferably 
have  a  thickness  not  greater  than  the  angles,  nor  more  than 
I  inch;  when  two  or  more  plates  are  used,  they  shall  have 
the  same  thickness,  or  shall  diminish  in  thickness  outwards 
from  the  angles,  except  the  first  plate  in  the  top  flange, 
which  shall  extend  the  full  length  of  the  flange,  and  may  be 
thinner  than  the  other  plates.  Other  plates  shall  extend 
12  inches  at  each  end  beyond  their  theoretical  ends.  Flange 
plates  shall  extend  beyond  the  outer  lines  of  rivets  not  more 
than  4  inches,  nor  more  than  eight  times  the  thickness  of  the 
thinnest  plate. 

61.  Flange  Splices. — Flange  members  of  girders  less 
than  70  feet  long  shall  not  be  spliced.  For  girders  longer  than 
70  feet,  each  flange  angle  shall  be  spliced  by  two  splice 
angles  each  having  a  cross-section  75  per  cent,  that  of  the 
flange  angle,  and  with  sufficient  rivets  on  each  side  of 
the  splice  to  fully  develop  the  stress  in  the  splice  angle. 
Flange  plates  shall  preferably  be  spliced  without  additional 
splice  plates,  by  continuing  the  outer  plates  beyond  their 
theoretical  ends  a  sufficient  distance  to  splice  the  lower 


§74 


BRIDGE  SPECIFICATIONS 


17 


plates.  When  splice  plates  are  not  in  direct  contact  with  the 
plates  they  splice,  the  calculated  number  of  rivets  shall  be 
increased  20  per  cent,  for  each  intervening  plate.  Only  one 

member  shall  be  spliced  at  any  section. 

\ 

62.  Riveting  of  Girders. —  Deck  girder  bridges  less 
than  70  feet  long  shall  preferably  be  riveted  up  complete 
before  shipping. 


DETAILS  OF  RIVETED  TRUSSES 

63.  Chord  Members. — The  chords  and  end  posts  shall 
be  composed  of  channels,  or  of  vertical  plates  and  flange 
angles,  connected  by  cover-plates  at  the  top  and  by  tie- 
plates  and  lattice  bars  at  the  bottom.  Gusset  plates  for  the 
connection  of  web  members  to  chords  shall  be  riveted  to 
the  inside  of  the  chords,  and  shall  be  designed  to  resist 
the  stresses  to  which  they  are  subjected. 

64.  Web  Members. — Web  members  shall  intersect  each 
other  and  the  chords  on  lines  passing  through  their  centers 
of  gravity,  and  shall  be  thoroughly  riveted  to  each  other  and 
to  the  connection  plates  at  every  intersection.  Web  mem¬ 
bers  shall  be  composed  of  symmetrical  sections,  preferably 
not  less  than  12  inches  in  width,  connected  by  web-plates  or 
by  tie-plates  and  lattice  bars.  The  clear  distance  between 
gussets  shall  be  not  more  than  i  inch  greater  than  the 
width  of  the  web  member  that  connects  to  them. 

65.  Connections  and  Splices. — Splices  of  chords  shall 
be  as  close  as  practicable  to  panel  points.  All  splices  of 
chords  and  connections  of  web  members  shall  have  enough 
rivets  to  develop  fully  the  stress  in  the  members.  If  a  splice 
occurs  at  a  joint,  that  part  of  the  gusset  in  contact  with  the 
chord  shall  be  counted  as  a  splice  plate. 

66.  Tension  Members. — Tension  members  shall  be  of 
the  same  general  form  as  compression  members.  The  use 
of  flat  bars  alone  for  riveted  tension  members  will  not 
be  allowed. 


135—3 


18 


BRIDGE  SPECIFICATIONS 


§74 

DETAILS  OF  PIN-CONNECTED  TRUSSES 

67.  Chord  Members. — The  top  chord  and  end  posts 
shall  be  composed  of  channels,  or  of  vertical  plates  with 
flange  angles,  connected  by  cover-plates  at  the  top  and  by 
tie-plates  and  lattice  bars  at  the  bottom,  or  by  tie-plates  and 
lattice  bars  at  both  top  and  bottom.  Splices  of  top  chords 
shall  be  as  close  as  practicable  to  panel  points,  and  shall 
have  enough  rivets  to  develop  the  stresses  fully.  The  bot¬ 
tom  chord  shall  be  composed  of  eyebars;  the  inside  bars  in 
the  two  end  panels  shall*  be  connected  to  each  other  by  dia¬ 
phragms  or  by  lattice  bars.  The  eyebars  shall  be  packed  on 
the  pins  as  narrow  as  possible;  those  in  any  panel  shall  not  be 
in  contact,  and  shall  not  diverge  from  the  center  line  of  truss 
by  more  than  tV  inch  per  foot. 

68.  Web  Members. — Web  members  shall  intersect  each 
other  and  the  chords  on  lines  passing  through  their  centers 
of  gravity,  and  pins  shall  be  located  at  the  intersections  of 
these  lines.  Compression  web  members  shall  be  composed 
of  symmetrical  sections,  preferably  not  less  than  12  inches  in 
width,  connected  by  web-plates  or  by  tie-plates  and  lattice  bars. 
Tension  web  members,  except  hip  verticals  and  subverticals, 
shall  be  composed  of  eyebars.  Hip  verticals  and  subverticals 

shall  be  of  the  same  general  form  as  compression  members. 

\ 

69.  Counters.  —  Counters  shall  be  adjustable  eyebars 
with  screw  ends  and  open  turnbuckles.  The  area  at  the  root 
of  an  upset  screw  end  shall  in  no  case  be  less  than  10  per 
cent,  greater  than  the  body  of  the  bar.  No  counter  shall 
have  a  sectional  area  of  less  than  3  square  inches. 

70.  Minimum  Eyebars. — No  eyebar  shall  be  less  than 
4  inches  in  width  or  less  than  f  inch  in  thickness. 

71.  Pins. — Pins  shall  be  not  less  than  3  inches  in 
diameter,  and  shall  project  i  inch  at  each  end  beyond  the 
outside  surfaces  of  the  members. 

72.  Riveted  Tension  Members. — Riveted  tension 
,  members  shall  have  a  net  section  back  of  pinholes  at  least 


§74 


BRIDGE  SPECIFICATIONS 


19 


equal  to  the  net  section  of  the  member,  and  through  pinholes 
at  least  25  per  cent,  greater. 

73.  Pin  Plates. — Where  necessary  for  section  or  bear¬ 
ing,  members  shall  be  reinforced  at  pinholes  by  pin  plates. 
Each  plate  shall  contain  sufficient  rivets  to  transmit  its  pro¬ 
portion  of  the  bearing  pressure  to  the  member.  One  plate 
on  each  side  shall  extend  at  least  6  inches  beyond  the  end 
of  the  tie-plate.  The  cross-section  of  a  compression  mem¬ 
ber  through  a  pinhole  shall  be  at  least  equal  to  that  of  the 
member. 


DETAILS  OF  STEEL  TRESTLES  (VIADUCTS) 

74.  Towers  and.  Main  Spans. — Steel  trestles  shall 
consist  of  riveted  spans  on  trestle  bents  braced  in  pairs  to 
form  towers.  Tower  spans  shall  be  not  less  than  30  feet 
long,  and  shall  be  riveted  to  the  tops  of  the  trestle  bents; 
main  spans  shall  be  riveted  to  the  tops  of  the  trestle  bents 
at  one  end,  and  bolted  to  them  at  the  other  through  expan¬ 
sion  holes.  In  single-track  trestles,  the  girders  shall  be  con¬ 
nected  to  the  tops  of  the  columns;  in  double-track  trestles, 
the  outer  lines  of  girders  or  trusses  shall  be  connected  to  the 
tops  of  the  columns,  and  the  inner  lines  to  cross-girders,  the 
ends  of  which  are  connected  to  the  tops  of  the  columns. 

75.  Trestle  Bents. — Trestle  bents  for  single-track  tres¬ 
tles  shall  be  not  less  than  8  feet  wide  on  top,  and  the  batter 
of  each  post  shall  be  not  less  than  1  horizontal  to  6  vertical. 
Trestle  bents  for  double-track  trestles  shall  be  not  less  than 
19  feet  6  inches  wide  on  top,  and  the  batter  of  each  post  shall 
be  not  less  than  1  horizontal  to  8  vertical.  On  curves,  towers 
shall  be  placed  so  that  the  center  lines  of  the  bents  are  at 
right  angles  to  the  chord  of  the  curve  between  bents. 

76.  Towers. — Towers  shall  be  divided  into  stories  not 
more  than  30  feet  in  height  by  horizontal  struts  and  diagonal 
bracing  between  the  columns. 

77.  Negative  Reactions.  —  In  estimating  negative 
(downward)  reactions  at  the  feet  of  the  columns,  the  weight 
of  train  shall  be  taken  as  800  pounds  per  linear  foot. 


20 


BRIDGE  SPECIFICATIONS 


74 


DETAILS  OF  BEARINGS 

78.  Bedplates. — The  ends  of  all  spans  and  the  bottoms 
of  columns  of  trestle  bents  shall  rest  on  bedplates  or  ped¬ 
estals,  and  shall  be  held  in  place  by  anchor  bolts.  Bedplates 
for  girders  and  stringers  shall  be  not  less  than  1  inch 
in  thickness,  and  for  trusses  and  columns  not  less  than 
l|-  inches.  Holes  for  anchor  bolts  may  be  i  inch  larger  in 
diameter  than  the  bolts. 

79.  Anchor  Bolts. — Anchor  bolts  shall  be  not  less 
than  1  inch  in  diameter  for  girders  and  stringers,  nor 
less  than  li  inches  for  trusses;  they  shall  be  set  in  holes 
drilled  in  the  masonry,  and  the  holes  shall  be  filled  with 
cement  grout.  Anchor  bolts  for  columns  having  a  negative 
reaction  shall  be  designed  to  resist  the  reaction,  and  shall  be 
built  in  a  mass  of  masonry  the  weight  of  which  is  not  less 
than  twice  the  estimated  reaction.  Anchor  bolts  in  expansion 
ends  shall  be  so  placed  that  the  ends  can  move  freely  in  the 
direction  of  expansion,  and  in  no  other  direction. 

80.  Pedestals. — Spans  over  75  feet  in  length  shall  have 
pin  bearings  and  pedestals  at  both  ends.  Pedestals  shall  be 
built  up  of  base  and  web  plates  not  less  than  i  inch  in 
thickness.  The  webs  shall  be  secured  to  the  base  plates  by 
angles  not  less  than  6  in.  X  4  in.  X  2  in.,  with  the'  6-inch  leg 
vertical,  and  the  webs  shall  be  connected  to  each  other. 
The  pedestals  shall  be  of  sufficient  height  to  distribute  the 
load  over  the  bearings. 

81.  Ends  of  Columns. — Caps  and  base  plates  shall  be 
connected  to  the  tops  and  bottoms,  respectively,  of  all  via¬ 
duct  columns,  by  means  of  horizontal  angles  not  less  than 
6  in.  X  4  in.  X  2  in.,  with  the  6-inch  leg  vertical  or  parallel  to 
the  batter  of  the  column. 

82.  Rollers. — Spans  over  75  feet  in  length  shall  have 
rollers  at  one  end.  Rollers  shall  be  not  less  than  3  inches 
in  diameter,  and  shall  be  turned  down  to  a  groove  i  inch 
deep  to  fit  guiding  strips  of  this  thickness  on  the  bearing 


§74 


BRIDGE  SPECIFICATIONS 


21 


plates  above  and  below  the  rollers.  Special  attention  shall 
be  given  to  roller  bearings,  so  that  they  will  not  hold  water, 
and  so  that  they  can  be  readily  cleaned. 

83.  Adjacent  Spans. — When  the  girders  or  trusses  of 
two  adjacent  spans  rest  on  the  same  pier,  the  bedplates  and 
pedestals  shall  be  entirely  independent  for  each  girder  or  truss. 

84.  Spans  on  Grade. — For  spans  without  rocker  bear¬ 
ings,  a  sole  plate  of  the  same  size  as  the  bedplate  shall  be 
riveted  to  the  bottom  of  the  span  at  each  end;  if  the  track  is 
on  a  grade,  the  sole  plate  shall  be  planed  to  bevel,  so  that 
the  lower  surface  will  be  level  when  the  floor  of  the  span  is 
parallel  to  the  jjrade. 


DETAILS  OF  BRACING 

85.  Independent  Bracing. — All  spans  shall  be  inde¬ 
pendently  braced;  no  bracing  shall  be  used  in  common  for 
any  two  adjacent  spans. 

86.  Style  of  Members. — Members  of  bracing  shall 
either  be  built-up  members  or  be  composed  of  simple  rolled 
shapes.  They  shall  intersect  each  other,  and  the  members 
to  which  they  connect,  on  lines  passing  as  nearly  as  practi¬ 
cable  through  their  centers  of  gravity,  and  shall  be  riveted 
to  each  other  and  to  connection  plates  at  every  intersection. 
No  member  shall  be  less  than  32  in.  X  3i  in.  X  t  in.,  and 
no  connection  shall  have  less  than  four  rivets. 

87.  Lateral  Bracing.— Top  and  bottom  lateral  bracing 
shall  be  provided  in  deck  and  through  bridges;  bottom  lateral 
bracing  in  half-through  bridges.  Lateral  bracing  shall  be 
riveted  to  the  stringers  of  the  floor  system  wherever  it  comes 
in  contact  with  them.  Deck  girders  shall  have  the  top  lateral 
bracing  so  arranged  that  the  length  of  the  flange  between 
lateral  connections  will  not  exceed  twelve  times  its  width.  If 
stringers  are  longer  than  twelve  times  the  width  of  the  flange, 
lateral  bracing  shall  be  riveted  to  their  upper  flanges. 

88.  Transverse  Bracing. — Deck  girder  bridges  shall 
have  transverse  frames,  of  the  same  depth  as  the  girders, 


22 


BRIDGE  SPECIFICATIONS 


§74 


riveted  to  the  stiffeners  near  the  ends,  and  at  other  points 
at  distances  apart  not  greater  than  15  feet.  If  stringers  are 
longer  than  twenty  times  the  width  of  the  flange,  transverse 
frames  shall  be  riveted  to  their  webs  at  the  intersections  of 
the  stringers  and  lateral  bracing.  Deck  truss  bridges  shall 
have  sway-bracing,  of  the  same  depth  as  the  trusses,  at 
every  panel  point. 

89.  Knee  Bracing. — Half-through  bridges  shall  have 
brackets  or  knee  braces  riveted  to  the  floorbeams  or  the 
tops  of  solid  floors,  and  to  the  webs  of  the  girders.  Knee 
braces  shall  fit  tight  under  the  top  flange  angles  of  girders, 
and  shall  be  as  wide  at  the  top  of  the  rail  as  the  clearance 
will  allow.  They  shall  be  so  arranged  that  the  distance 
between  them  shall  not  exceed  twelve  times  the  width  of 
the  top  flange  of  the  girder. 

90.  Portal  Bracing. — Through  bridges  shall  have 
portals  and  portal  brackets,  and  intermediate  brackets  at 
each  transverse  strut  of  the  upper  lateral  bracing.  Portals 
shall  be  as  deep  as  the  specified  clearance  will  allow. 
Where  the  headroom  above  the  track  is  25' feet  or  more, 
sway  frames  shall  be  provided  at  every  panel  point  of  the 
top  chord;  they  shall  be  as  deep  as  the  required  headroom 
will  allow. 


DESIGN  OF  HIGHWAY  AND  STREET-RAII/WAY 

BRIDGES 


GENERAL  DIMENSIONS 

91.  Kinds  of  Bridges. — The  following  kinds  of  bridges 
shall  preferably  be  used: 

For  spans  less  than  35  feet  in  length,  rolled  beams. 

For  spans  from  35  to  100  feet  in  length,  plate  girders. 

For  spans  from  100  to  150  feet  in  length,  riveted  trusses. 

For  spans  longer  than  150  feet,  pin-connected  trusses. 

If,  for  any  reason,  it  is  desired  to  depart  more  than  10  feet 
from  these  limits,  permission  in  writing  must  be  obtained 
from  the  Engineer. 


§74 


BRIDGE  SPECIFICATIONS 


23 


92.  Panel  Lengths  and  Depths. — The  depth  of  girders 
shall  preferably  be  not  less  than  one-twelfth  the  span. 
Panel  lengths  shall  preferably  be  from  15  to  30  feet,  and  in 
truss  bridges  the  panel  lengths  and  depths  shall  be  so  chosen 
that  the  inclined  web  members  shall  make  an  angle  with  the 
lower  chord  of  not  less  than  50°.  The  depth  of  I  beams 
shall  in  no  case  be  less  than  one-thirtieth  of  the  span. 

93.  Spacing  of  Stringers,  Girders,  and  Trusses. 
For  bridges  carrying  only  a  railway  track,  stringers  of  floor 
systems,  and  deck  girders  less  than  70  feet  long,  shall  be 
spaced  6  feet  6  inches  center  to  center.  Deck  girders  over 
70  feet  long  shall  be  spaced  6  inches  farther  apart  for  each 
10  feet  increase  in  length.  Stringers,  girders,  and  trusses  in 
bridges  carrying  both  railways  and 
highways,  or  highways  only,  shall  be 
arranged  to  accommodate  the  actual 
traffic,  and  shall  be  adapted  to  local 
conditions.  Trusses  shall  be  spaced 
not  less  than  one-twentieth  of  the  span. 

94.  Clearance. — No  part  of  any 

bridge  shall  come  closer  to  the  center 
line  of  the  nearest  track  than  is  shown 
in  outline  in  Fig.  4.  If  a  track  is  on  a 
curve,  I  inch  additional  clearance  for 
each  degree  of  curvature  shall  be  pro¬ 
vided  on  the  outside  of  the  curve,  and 
on  the  inside  of  the  curve  i  inch  addi-  5-5 

tional  clearance  for  each  degree  of  Fig.  4 

curvature,  and  2  inches  for  each  inch  of  superelevation  of 
track.  All  through  highway  bridges  carrying  railways  shall 
have  a  clear  headroom  of  15  feet  at  a  distance  of  3  feet  from 
the  wheel-guards;  those  carrying  highways  only  shall  have  a 
clear  headroom  of  not  less  than  13  feet  at  a  distance  of  3  feet 
from  the  wheel-guards. 

95.  Spacing  of  Tracks. — When  there  is  more  than 
one  track,  the  tracks  shall  be  assumed  as  10  feet  center 
to  center. 


24 


BRIDGE  SPECIFICATIONS 


§74 


LOADING 

96.  Loads. — Bridges  carrying  highways  only  shall  be 
designed  to  resist  pro'perly  the  stresses  caused  by  the 
following  forces:  dead  load ,  live  or  moving  load ,  and  wind 
pressure.  Bridges  carrying  railways  alone  or  in  connection 
with  highways  shall  be  designed  to  resist  properly  the 
stresses  caused  by  the  forces  mentioned  and,  in  addition, 
those  caused  by  impact  and  vibration ,  centrifugal  force ,  and 
the  longitudinal  force  due  to  suddenly  stopping  cars. 

97.  Dead  Load. — The  dead  load  shall  consist  of  the 
estimated  weight  of  the  entire  structure.  The  actual  weight 
of  the  floor  and  track,  if  any,  shall  be  computed;  timber 
shall  be  assumed  to  weigh  4i  pounds  per  board  foot.  For 
bridges  carrying  railways  alone,  the  weight  of  rails,  ties,  etc. 
may  be  taken  as  300  pounds  per  linear  foot  of  track.  In 
truss  bridges,  one-half  the  weight  of  the  trusses  shall  be 
assumed  as  applied  at  the  loaded  chord,  and  one-half  at  the 
unloaded  chord;  the  entire  weight  of  floor  shall  be  assumed 
as  applied  at  the  loaded  chord. 

98.  Live  Load. — The  live  load  shall  consist  of  the 
estimated  maximum  moving  loads  that  the  bridge  is  expected 
to  carry.  It  will  depend  on  the  amount  and  kind  of  traffic 
to  which  the  bridge  is  to  be  subjected,  and  shall  in  general 
be  assumed  as  follows: 

1.  For  City  Bridges  Subject  to  Heavy  Loads. — For  the 
hip  verticals,  subverticals,  short  diagonals,  floor  hangers, 
and  floor  members  of  all  spans,  either  a  uniform  load  of 
100  pounds  per  square  foot  on  all  parts  of  the  floor,  or  a 
steam  road  roller  weighing  20  tons  distributed  as  repre¬ 
sented  in  Fig.  5.  For  the  girders  or  trusses  of  all  spans  up 
to  100  feet,  a  uniform  load  of  100  pounds  per  square  foot 
on  the  entire  surface  of  the  floor;  of  all  spans  over  200  feet, 
80  pounds  per  square  foot;  and  of  intermediate  spans,  pro¬ 
portional  intermediate  values.  (Between  100  and  200  feet, 
the  uniform  load  decreases  1  pound  per  square  foot  for  each 
5  feet  increase  in  span.) 


§74 


BRIDGE  SPECIFICATIONS 


25 


2.  For  Bridges  in  the  Suburbs  of  Cities  and  in  Well- 
Set  tied  Town  Districts. — For  the  hip  verticals,  subverticals, 
short  diagonals,  floor  hangers,  and  floor  members  of  all 
spans,  either  a  uniform  load  of  100  pounds  per  square  foot 
on  all  parts  of  the  floor,  or  a  steam  road  roller  weighing 
15  tons  distributed  as  represented  in  Fig.  6.  For  the  girders 
or  trusses  of  all  spans  up  to  100  feet,  a  uniform  load  of 
80  pounds  per  square  foot  on  the  entire  surface  of  the 


t- 


2-0 
12000 


„  /  „  // 
-2-0  - 


lb. 


VI 

! 

* 


- 1 


/4000  A 5. 


10000  lb. 


_  /  -// 
-2-0  — 


10000 


2-0- 


lb. 


§ 

NJ 

I 


Si 

'I 


—  2-0,L-* 

-  C-6^ 

~/-6"» 

* — 2^-0"- — * 

Fig.  5 


Fig.  6 


floor;  of  all  spans  over  200  feet,  60  pounds  per  square  foot; 
and  of  intermediate  spans,  proportional  intermediate  values. 
(Between  100  and  200  feet  the  uniform  load  decreases 
1  pound  per  square  foot  for  each  5  feet  increase  in  span.) 

3.  For  Bridges  in  Country  Districts  and  in  Thinly  Settled 
Communities. — For  the  hip  verticals,  subverticals,  short 
diagonals,  floor  hangers,  and  floor  members  and  connections 


26 


BRIDGE  SPECIFICATIONS 


§74 


of  all  spans,  either  a  uniform  load  of  80  pounds  per  square 
foot  on  all  parts  of  the  floor,  or  a  steam  road  roller  weigh¬ 
ing  15  tons  distributed  as  represented  in  Fig.  6.  For  the 
girders  or  trusses  of  all  spans  up  to  75  feet,  a  uniform  loa^ 
of  80  pounds  per  square  foot  on  the  entire  surface  of  the 
floor;  of  all  spans  over  200  feet,  55  pounds  per  square  foot; 
and  of  intermediate  spans,  proportional  intermediate  values. 
(Between  75  and  200  feet,  the  uniform  load  decreases 
1  pound  per  square  foot  for  each  5  feet  increase  in  span.) 

4.  For  All  Bridges  Carrying  Street  Railway,  or  That  Are 
Expected  to  Carry  Street  Railway  in  the  Near  Future . — For 

the  hip  verticals,  sub¬ 
verticals,  short  diag¬ 
onals,  floor  hangers, 
and  floor  members  of 
all  spans,  and  for  the 
girders  of  spans  less 
than  75  feet,  an  electric  car  on  each  track  weighing  40  tons, 
distributed  as  shown  in  Fig.  7;  for  the  web  members  of  spans 
75  to  100  feet  in  length,  1,600  pounds  per  linear  foot,  and  of 
all  spans  over  100  feet,  a  floorbeam  load  of  (1,600  p)  pounds 


o 

o 

o 

o 

<N 


o 

o 

o 

o 

OJ 


o 

o 

o 

o 

<N 


o 

o 

o 

o 

CN 


K 

)  t 

)  C 

)  c 

1 

- —  5'-* 

—  /S'  — * 

—  5'— 

Fig.  7 


for  each  track  at 


floorbeams  (/being  the  panel  length, 


in  feet);  for  the  chord  members  of  spans  75  feet  in  length, 
1,600  pounds  per  linear  foot;  of  spans  275  feet  or  more  in 
length,  1,000  pounds  per  linear  foot;  and  of  intermediate 
spans,  proportional  intermediate  values.  (Between  75  and 
275  feet,  the  uniform  load  decreases  3  pounds  for  each  1  foot.) 

5.  For  Bridges  Carrying  Both  Highway  and  Street  Rail¬ 
way. — The  live  load  shall  consist  of  the  electric  car  or  uni¬ 
form  load  given  in  item  4  above,  together  with  the  uniform 
loads  given  in  items  1,  2,  or  3  covering  the  entire  floor, 
except  a  width  of  10  feet  for  each  track. 


99.  Impact  and  Vibration. — To  provide  for  impact  and 
vibration  in  bridges  carrying  street  railways,  an  amount  /  is 
to  be  added  to  the  stress  or  bending  moment  caused  by  the 
car  in  each  member,  as  given  by  the  following  formulas: 


§74 


BRIDGE  SPECIFICATIONS 


27  * 


For  counters,  hip  verticals,  subverticals,  short  diagonals, 
floor  hangers,  floor  members  and  connections,  members  sub¬ 
ject  to  reversal  of  stress,  and  all  other  members  for  which 
L  is  less  than  25  feet, 


For  all  members  for  which  L  is  greater  than  200  feet, 


I  =-hs 


Here,  S'  =  maximum  live-load  stress  or  bending  moment 


in  the  member  due  to  load  on  car  track; 


L  —  length  of  track,  in  feet,  that  must  be  loaded  in 
order  to  obtain  the  value  ,5. 


100.  Wind  Pressure. — Wind  pressure  shall  be  assumed 
in  girder  bridges  as  50  pounds  per  square  foot  on  the  exposed 
area  of  one  girder,  and  in  truss  bridges  as  50  pounds  per 
square  foot  on  twice  the  exposed  area  of  one  truss  together 
with  the  exposed  area  of  the  floor.  In  designing  the  stringers 
of  floor  systems  in  bridges  carrying  railway,  the  wind  pres¬ 
sure  on  the  cars  shall  be  assumed  to  be  250  pounds  per  linear 
foot,  applied  6  feet  above  the  rail,  and  the  center  of  moments 
for  the  increase  in  load  on  the  leeward  stringer  shall  be 
taken  at  the  top  of  the  rail. 

101.  Centrifugal  Force. — In  bridges  on  curves,  the 
centrifugal  force  F  caused  by  electric  cars  shall  be  assumed 
to  act  5  feet  above  the  rail,  and  shall  be  found  by  the  formula 


D  =  degree  of  curve; 
W  =  live  load. 


in  which 


102.  Suddenly  Stopping  Cars. — The  longitudinal 
force  due  to  a  suddenly  stopping  car  shall  be  taken  equal 
to  16,000  pounds  applied  at  the  top  of  the  rail. 


28 


BRIDGE  SPECIFICATIONS 


§74 


DESIGN  OF  MEMBERS 


103.  Working  Stresses. — All  parts  shall  be  so  designed 
that  the  sum  of  the  maximum  stresses  shall  not  cause  the 
intensities. of  stress  to  exceed  the  following  values,  in  pounds 
per  square  inch: 

Tension  on  net  section,  16,000. 

Compression  on  gross  section, 

16,000 

r 

l  H - - - 

18,000  r2 

in  which  /  =  unsupported  length  of  member,  in  inches; 
r  =  least  radius  of  gyration,  in  inches. 

In  half-through  truss  bridges,  the  entire  length  of  the 
upper  chord  shall  be  considered  unsupported  laterally,  the 
stiffening  effect  of  knee  braces  being  ignored. 

Shear  on  net  sections  of  web  plates, 

12,000 


1  + 


(P 


3,000  f 

in  which  t  =  thickness  of  the  web,  in  inches; 

d  =  clear  distance,  in  inches,  between  stiffeners  or 
flange  angles,  whichever  is  the  smaller. 

The  intensity  of  shearing  stress  found  by  dividing  the  total 
vertical  shear  by  the  gross  area  of  cross-section  of  the  web 
shall  in  no  case  exceed  9,000. 

Shear  on  shop  rivets  and  pins,  11,000. 

Shear  on  field  rivets  and  turned  bolts,  9,000. 

Bending  on  pins,  22,000. 

Bending  on  rolled  sections  and  plate  girders: 

Tension,  16,000. 

Compression,  when  unsupported  length  /  of  compres¬ 
sion  flange  is  not  greater  than  twenty  times  the 
width  w,  16,000. 

Compression,  when  /  is  greater  than  20  w. 

20,000  -  200  - 

w 

Bearing  on  shop  rivets  and  pins,  22,000. 


74 


BRIDGE  SPECIFICATIONS 


29 


Bearing  on  field  rivets,  turned  bolts,  and  ends  of  stiffeners, 
18,000. 

Bearing  on  masonry: 

Sandstone  and  limestone,  300. 

Cement  concrete,  400. 

Granite,  500. 

The  bearing  on  rollers  shall  not  exceed  600  D  pounds  per 
linear  inch  of  roller,  in  which  D  is  the  diameter  of  roller,  in 
inches. 

Bending  on  fir,  yellow-pine,  and  white-oak  beams,  1,200. 

Bending  on  white-pine  and  spruce  beams,  1,000. 

104.  Data. — The  following  general  dimensions  shall 
first  be  calculated  or  assumed: 

Length  of  trusses,  center  to  center  of  end  pins  or  pedestals. 

Length  of  girders,  center  to  center  of  bearings. 

Length  of  floorbeams,  center  to  center  of  girders  or 
trusses. 

,  » 

Length  of  stringers,  center  to  center  of  floorbeams. 

* 

Depth  of  trusses  and  girders,  center  to  center  of  gravity 
of  chords  or  flanges. 

105.  Compression.  Members. — Pin  and  bolt  holes 
shall  be  deducted  from  the  gross  section  of  compression 

members.  The  value  of  -  will  preferably  be  from  40  to  60, 

r 

and  must  not  exceed  100  for  main  members,  nor  120  for 
members  of  lateral  systems.  Splices  in  compression  mem¬ 
bers  shall  have  sufficient  rivets  to  develop  fully  the  stresses 
in  the  members. 

106.  Tension  Members. — The  net  section  of  a  riveted 
tension  member  shall  be  determined  by  deducting  from  the 
gross  section  the  area  of  cross-section  of  the  greatest  num¬ 
ber  of  pin,  bolt,  or  rivet  holes  that  can  be  cut  by  a  plane  at 
right  angles  to  the  member.  In  addition,  for  rivets  f  inch 
in  diameter  and  larger,  there  shall  be  deducted  each  hole 
whose  center  lies  within  f  inch  of  the  cutting  plane  and  a 
proportional  part  of  each  hole  whose  center  lies  within 
2f  inches;  and,  for  rivets  f  inch  in  diameter  and  smaller, 


30 


BRIDGE  SPECIFICATIONS 


§74 


there  shall  be  deducted  each  hole  whose  center  lies  within 
2  inch  and  a  proportional  part  of  each  hole  whose  center  lies 
within  2  inches.  Rivet  holes  shall  be  taken  i  inch  larger  in 
diameter  than  the  rivets. 

i 

107.  Reversal  of  Stress. — Members  subject  to  both 
tension  and  compression  shall  be  designed  to  resist  each 
stress  plus  eight-tenths  of  the  other  stress. 

108.  Combined  Stresses. — Members  subject  to  trans¬ 
verse  stresses  in  addition  to  the  direct  stresses  shall  be 
designed  for  both  kinds  of  stress. 

109.  Bearing  Values  of  Rivets. — In  calculating  the 
bearing  value  of  a  rivet,  the  area  subjected  to  stress  shall  be 
taken  equal  to  the  product  of  the  thickness  of  the  plate  and 
the  diameter  of  the  rivet  before  driving,  that  is,  the  nominal 
diameter.  The  value  of  countersunk  rivets  shall  not  be 
counted. 

•  . 

110.  Floor  Stringers. — In  bridges  with  steel  stringers, 
each  stringer  shall  be  designed  to  support  one-half  the  load 
on  a  front  wheel  of  a  steam  roller  and  one-half  the  load  on 
one  rear  roller,  forming  a  system  of  two  concentrated  loads. 
In  bridges  with  wooden  joists,  the  loads  on  each  roller  of  a 
steam  road  roller  may  be  assumed  to  be  distributed  over  a 
width  12  inches  greater  than  the  width  of  the  roller,  and  the 
portion  that  goes  to  each  stringer  or  joist  calculated  on 
this  basis. 


GENERAL  DETAILS 

111.  Details  and  Connections. — Special  attention 
shall  be  given  to  all  details  and  connections,  which  shall 
always  be  of  greater  strength  than  the  body  of  the  member. 
All  details  shall  be  accessible  for  inspection,  cleaning,  and 
painting.  Details  that  permit  the  collection  of  water  shall 
be  avoided  if  possible;  if  used,  they  shall  be  provided  with 
drainage  holes  or  filled  with  cement  concrete. 

112.  Minimum  Thickness. — No  material  less  than 
re  inch  thick  shall  be  used  except  for  latticing  and  fillers, 


§74 


BRIDGE  SPECIFICATIONS 


31 


and  for  webs  of  channels,  which  may  be  i  inch  thick.  If  the 
bridge  is  over  a  steam  railroad,  no  material  less  than  f  inch 
thick  shall  be  used  below  the  floor,  except  for  buckled  plates, 
for  which  -r6-inch  material  may  be  used  under  sidewalks. 

113.  Single  Angles. — Members  or  sides  of  members 
composed  of  single  angles  shall  have  both  legs  of  each 
angle  connected  at  the  ends,  or  only  75  per  cent,  of  the 
section  shall  be  counted.  No  angle  shall  be  smaller  than 
2}  in.  X  2i  in.  X  in.,  nor  be  connected  by  less  than  three 
rivets,  except  for  unimportant  details. 

114.  Sizes  of  Rivets. — Rivets  shall  generally  be  either 
i  inch  or  f  inch  in  diameter.  The  diameter  of  the  rivet  shall 
n6t  be  greater  than  one-quarter  the  width  of  the  bar  or  angle 
through  which  it  passes,  except  for  unimportant  details, 
where  i-inch  rivets  may  be  used  in  3-inch  angles,  and  i-inch 
rivets  in  22-inch  angles. 

115.  Spacing  of  Rivets. — The  distance  center  to  center 
of  rivet  holes  shall  be  not  less  than  three  times  the  diameter 
of  the  rivets,  nor  more  than  6  inches  in  any  line.  The  cen¬ 
ters  of  rivet  holes  shall  not  be  closer  to  the  edge  of  any 
piece  than  li  times  the  diameter. of  the  rivet.  The  spacing 
of  rivets  at  the  ends  of  compression  members  shall  not 
exceed  four  times  the  diameter  of  the  rivet  for  a  distance 
equal  to  the  width  of  the  member.  For  the  remainder  of  the 
length  of  compression  members,  the  distance  center  to  center 
of  rivets  shall  be  not  greater  than  sixteen  times  the  thickness 
of  the  thinnest  outside  plate. 

116.  Compression  Members. — In  compression  mem¬ 
bers,  the  material  shall  be  concentrated  at  the  sides  as  much 
as  possible.  The  unsupported  width  of  plates  shall  not 
exceed  thirty  times  their  thickness  for  web-plates,  nor  forty 
times  for  cover-plates  of  chords  and  end  posts.  No  closed 
sections  will  be  allowed. 

117.  Tie-Plates  and  ^Lattice  Bars. — The  open  sides 
of  all  built-up  members  shall  be  stiffened  by  means  of  tie- 
plates  and  lattice  bars.  The  length  of  tie-plates  shall  be  not 


32 


BRIDGE  SPECIFICATIONS 


74 


less  than  their  width.  Double  latticing  shall  preferably  make 
an  angle  of  about  45°  with  the  axis  of  the  member,  and  the 
bars  shall  be  riveted  where  they  cross  each  other.  Single 
latticing  shall  preferably  make  an  angle  of  about  60°  with 
the  axis  of  the  member.  The  thickness  of  tie-plates  shall 
be  not  less  than  one-fortieth  the  distance  between  their  rivet 
lines;  the  thickness  of  bars  in  single  latticing  shall  be  not 
less  than  one-fortieth,  and  in  double  latticing  one-sixtieth 
of  the  distance  between  the  rivets  in  their  ends.  Lattice 
bars  shall  be  not  less  than  2i  inches  wide  for  members  up 
to  9  inches,  not  less  than  2i  inches  for  members  from  9  to 
15  inches,  nor  less  than  3  inches  for  members  more  than 
15  inches  in  width  or  depth. 

118.  Expansion. — Provision  for  expansion  and  contrac¬ 
tion  shall  be  made  at  the  rate  of  1  inch  for  every  100  feet 
of  span. 

119.  Camber. — All  trusses  shall  be  cambered  by  giving 
the  panels  of  the  top  chord  an  excess  of  length  in  the  pro¬ 
portion  of  i  inch  for  each  10  feet.  Plate  girders  shall  not 
be  cambered. 


DETAILS  OF  FLOOR  SYSTEMS 

120.  Wooden  Floors. — In  bridges  constructed  solely 
for  street-railway  purposes,  ties  shall  be  of  yellow  pine  not 
less  than  5  inches  wide,  7  inches  deep,  and  10  feet  long,  and 
shall  be  framed  to  62  inches  over  bearings  for  stringers  and 
girders  6  feet  6  inches  center  to  center.  For  girders  over 
6  feet  6  inches  center  to  center,  the  depth  of  tie  shall  be 
increased  2  inch  for  each  6-inch  increase  in  the  spacing  of 
the  girders.  Ties  shall  be  spaced  not  more  than  12  inches 
center  to  center,  and  every  fourth  tie  shall  be  fastened  at 
both  ends  to  the  stringers  or  girders  by  i-inch  bolts.  Guard 
timbers  of  yellow  pine  not  less  than  6  in.  X  6  in.,  framed  to 
4  inches  over  ties,  shall  be  bolted  by  1-inch  bolts  to  the  ties 
that  are  bolted  to  the  stringers,  and  so  that  the  inner  edge  of 
the  guard  timber  shall  be  4  feet  from  the  center  of  the  track. 
Guard  timbers  shall  extend  over  all  piers  and  abutments. 


§74 


•  BRIDGE  SPECIFICATIONS 


33 


Superelevation  of  rails,  on  curves  shall  be  provided  for  as 
may  be  required  in  each  case. 

121.  In  bridges  with  wooden  floors  constructed  for  com¬ 
bined  street-railway  and  highway  purposes,  the  rails  shall 
preferably  be  supported  on  yellow-pine  ties  not  less  than 
6  in.  X  6  in.  in  size,  nor  less  than  8  feet  long,  spaced  not 
over  15  inches  center  to  center  and  resting  on  the  stringers. 
Longitudinal  nailing  pieces  not  over  2  feet  apart  shall  be 
spiked  to  the  top  of  the  tie;  they  shall  be  not  less  than 
3  inches  wide,  and  of  sufficient  height  to  bring  the  top  of 
the  plank  floor  level  with  the  top  of  the  rails.  A  plank  floor 
not  less  than  2  inches  thick,  preferably  of  spruce  or  oak, 
shall  be  nailed  to  the  nailing  pieces. 

122.  For  bridges  in  country  districts  and  in  thinly  settled 
communities,  the  highway  portion  of  the  floor  shall  preferably 
consist  of  one  layer  of  white-oak  plank  not  less  than  3  inches 
in  thickness  laid  at  right  angles  to  the  trusses  or  girders,  and 
with  joints  about  i  inch  open.  Wooden  stringers  not  less 
than  3  in.  X  12  in.  or  steel  beams  with  wooden  nailing  pieces 
shall  be  used,  and  the  former  shall  be  spaced  not  over  2  feet 
6  inches  center  to  center.  In  general,  the  width  of  wooden 
stringers  shall  be  not  less  than  one-fourth  of  the  depth. 
The  plank  floor  shall  be  securely  spiked  to  the  stringers. 

123.  For  bridges  in  the  suburbs  of  cities,  in  well-settled 
town  districts,  and  in  some  cases  for  city  bridges  not  subject 
to  heavy  loads,  the  highway  portion  of  the  floor  shall  prefer¬ 
ably  consist  of  two  layers  of  plank;  the  lower  layer  shall  be 
of  white  oak  not  less  than  3  inches  in  thickness,  and  shall  be 
laid  diagonally  with  joints  not  over  i  inch  open;  the  upper 
layer  shall  be  of  white  oak  or  spruce  2  inches  thick,  laid 
tight  at  right  angles  to  the  girders  or  trusses  and  securely 
spiked  to  the  lower  layer.  Wooden  stringers,  as  before,  may 
be  used,  but  steel  stringers  with  wooden  nailing  pieces  shall 
have  the  preference.  When  one  layer  of  floor  plank  is  used, 
the  distance,  in  feet,  between  the  centers  of  joists  or  nailing 
pieces  shall  not  be  greater  than  the  thickness  of  the  plank,  in 
inches.  When  more  than  one  layer  is  used,  the  clear  distance, 


BRIDGE  SPECIFICATIONS 


34 


§74 


in  feet,  between  joists  or  nailing-  pieces  shall  not  be  greater 
than  the  thickness  of  the  lower  layer,  in  inches. 

124.  Paved  Floors. — For  city  bridges  subject  to  heavy 
loads,  the  floor  shall  preferably  consist  of  prepared  wooden 
blocks,  asphalt,  brick,  or  granite  blocks.  Wooden  blocks 
shall  be  given  the  preference;  granite  blocks  shall  be  used 
only  in  the  immediate  vicinity  of  warehouses,  docks,  or 
freight  houses,  where  the  traffic  is  exceedingly  heavy  and 
continuous.  Paved  floors  shall  be  supported  on  buckled 
plates  securely  riveted  to  the  upper  flanges  of  stringers  and 
to  the  floorbeams.  Buckled  plates  shall  be  laid  with  the 
buckle  hanging  down,  and  shall  be  covered  with  cement  con¬ 
crete  having  a  thickness  not  less  than  3  inches  under  the 
roadway  nor  less  than  2  inches  under  the  sidewalk.  Between 
the  concrete  and  the  paving  there  shall  be  spread  a  cushion 
coat  of  clean,  sharp  sand,  perfectly  free  from  moisture,  to 
an  even  thickness  of  1  inch.  Open  joints  between  blocks 
shall  be  filled  with  cement  grout  or  coal-tar  pitch. 

125.  Wheel-Guards. — In  bridges  with  wooden  floors,  a 
wheel-guard  of  timber  not  less  than  6  inches  wide  and  4  inches 
thick  shall  be  placed  longitudinally  on  the  floor.  The  upper 
edge  of  the  wheel-guard  shall  be  6  inches  from  the  surface  of 
the  floor.  The  edge  of  the  guard  toward  the  roadway  shall 
be  6  inches  from  the  clearance  line  of  the  trusses  or  girders. 
In  bridges  with  paved  floors,  a  metal  or  stone  wheel-guard 
shall  be  provided;  it  shall  be  6  inches  high  and  at  least 
6  inches  outside  of  the  clearance  line  of  the  trusses  or  girders. 

126.  Floor  Connections. — Stringers  shall  be  at  right 
angles  to  the  floorbeams,  and  shall  be  riveted  to  the  floor- 
beam  webs.  If  possible,  the  stringers  shall  also  rest  on 
shelf  angles  riveted  to  the  wTebs  of  the  floorbeams.  Floor- 
beams  shall  preferably  be  riveted  to  the  webs  of  the  girders 
in  half-through  girder  bridges,  and  to  the  vertical  posts  or 
web  connection  plates  in  through  truss  bridges;  in  deck  truss 
bridges,  the  floorbeams  shall  either  be  riveted  to  the  trusses, 
as  in  through  bridges,  or  rest  on  the  top  chords.  Where 
sidewalks  are  supported  outside  the  girders  or  trusses,  the 


§74 


BRIDGE  SPECIFICATIONS 


35 


fioorbeams  shall  be  extended  under  the  sidewalks,  or  side¬ 
walk  brackets  shall  be  riveted  to  the  outsides  of  the  posts, 
and  their  top  flanges  connected  to  those  of  the  fioorbeams. 

The  connection  angles  of  stringers  to  fioorbeams  and 
of  fioorbeams  to  girders  or  trusses  shall  be  not  less  than 
3  in.  X  3  in.  X  Te  in.  The  fillers  under  connection  angles 
shall  be  twice  as  wide  as  the  adjacent  leg  of  the  angle,  and 
shall  have  two-thirds  as  many  rivets  through  the  project¬ 
ing  portion  as  through  the  portion  under  the  angle. 

127.  Hand  Railing. — A  suitable  hand  railing  or  fence 
shall  be  placed  at  each  side  of  the  bridge.  The  railing  shall 
be  not  less  than  3  feet  6  inches  above  the  top  of  the  floor, 
and  have  not  more  than  6  inches  clearance  beneath  it. 


DETAILS  OF  PLATE  GIRDERS 

128.  Stiffeners. — Webs  shall  have  stiffeners  over  bear¬ 
ing  points,  at  points  of  local  concentrated  loadings,  and  at 
intervals  not  greater  than  the  depth  of  the  girder  nor  more 
than  6  feet.  Near  the  ends,  the  spacing  of  stiffeners  shall 
be  one-third  to  one-half  the  depth.  Stiffeners  shall  be  com¬ 
posed  of  two  angles,  one  on  each  side  of  the  web,  and  shall 
fit  tight  between  the  horizontal  legs  of  the  flange  angles. 
For  girders  having  flange  angles  with  outstanding  or  hori¬ 
zontal  legs  5  inches  in  width,  stiffeners  shall  be  not  less  than 
3^  in.  X  3i  in.  X  re  in.;  with  outstanding  legs  6  inches  in 
width,  not  less  than  4  in.  X  3i  in.  X  Te  in.;  with  outstanding 
legs  8  inches  in  width,  not  less  than  5  in.  X  3i  in.  X  1  in. 
Rivets  in  stiffeners  shall  be  spaced  not  over  4}  inches  apart 
for  a  distance  of  18  inches  at  each  end,  and  not  over  6  inches 
apart  for  the  remaining  portion.  When  the  clear  vertical 
distance  between  flange  angles  is  less  than  fifty  times  the 
thickness  of  the  web,  stiffener  angles  may  be  omitted, 
except  over  bearings.  Stiffeners  over  bearings  shall  be 
designed  to  resist  the  reactions. 

129.  Web  Splices. — Web-plates  shall  be  spliced  by  one 
or  more  plates  on  each  side,  the  plates  on  each  side  to  have 


36 


BRIDGE  SPECIFICATIONS 


§74 


a  section  equal  to  three-fourths  that  of  the  web,  and  a  pair  of 
stiffeners  placed  outside  the  plates.  There  shall  be  not 
less  than  two  rows  of  rivets  3|  inches  apart  on  each  side 
of  the  splice.  Rivets  in  splice  plates  shall  be  spaced  not 
over  3|  inches  apart  for  a  distance  of  14  inches  at  top  and 
bottom,  and  not  over  5  inches  between.  Web  splices  shall 
be  designed  for  the  same  resisting  moment  as  the  web. 


130.  Flange  Rivets. — The  pitch  of  rivets  connecting 
the  flange  angles  to  the  web  at  any  point  shall  be  calculated 


by  means  of  the  formula  p  = 


(see  Art.  57). 
V 


When 


the  ties  of  street-railway  bridges  rest  on  the  top  flanges  of 
deck  girders,  the  pitch  of  the  rivets  in  the  top  flange  shall 
be  90  per  cent,  of  the  calculated  pitch.  The  rivets  con¬ 
necting  flange  plates  to  flange  angles  shall  have  the  same 
spacing  as,  and  stagger  with,  those  connecting  the  flange 
angles  to  the  web.  The  spacing  of  rivets  in  plate-girder 
flanges  shall  in  no  case  exceed  6  inches. 


131.  '  Flanges. — Flanges  shall  be  designed  for  the  net 
section  of  the  bottom  flange,  and  the  gross  section  of  the  top 
flange.  One-eighth  of  the  web  shall  be  considered  as  part  of 
the  flange  section.  Girders  with  deep  webs  may  have  flanges 
composed  of  vertical  as  well  as  horizontal  flange  plates. 

132.  Flange  Angles. — Flange  angles  shall  preferably 
be  of  large  sections;  in  general,  not  less  than  one-third  to 
one-half  the  flange  section  shall  be  composed  of  angles. 

133.  Flange  Plates. — Flange  plates  shall  preferably 
have  a  thickness  not  greater  than  the  angles  nor  more  than 
f  inch.  When  two  or  more  plates  are  used,  they  shall  have 
the  same  thickness,  or  shall  diminish  in  thickness  outwards 
from  the  angles,  except  the  first  plate  of  the  top  flange,  which 
shall  extend  the  full  length  of  the  flange  and  may  be  thinner 
than  the  other  plates.  Other  plates  shall  extend  12  inches  at 
each  end  beyond  their  theoretical  ends.  Flange  plates  shall 
extend  beyond  the  outer  lines  of  rivets  not  more  than  4  inches 
nor  more  than  eight  times  the  thickness  of  the  thinnest  plate. 


§74 


BRIDGE  SPECIFICATIONS 


37 


134.  Flange  Splices. — Flange  members  of  girders  less  . 
than  70  feet  long  shall  not  be  spliced.  For  girders  longer 
than  70  feet,  each  flange  angle  shall  be  spliced  by  two  splice 
angles,  each  having  a  cross-section  75  per  cent,  of  that  of  the 
flange  angle,  and  with  sufficient  rivets  on  each  side  of  the 
splice  to  develop  fully  the  stress  in  the  splice  angle.  Flange 
plates  shall  preferably  be  spliced  without  additional  splice 
plates,  by  continuing  the  outer  plates  beyond  their  theoret¬ 
ical  ends  a  sufficient  distance  to  splice  the  lower  plates.  When 
splice  plates  are  not  in  direct  contact  with  the  plates  they 
splice,  the  calculated  number  of  rivets  shall  be  increased 
20  per  cent,  for  each  intervening  plate.  Only  one  member 
shall  be  spliced  at  any  section. 


DETAILS  OF  RIVETED  TRUSSES 

135.  Chord  Members. — The  chords  and  end  posts  shall 
be  composed  of  channels,  or  of  vertical  plates  and  flange 
angles,  connected  by  cover-plates  at  the  top,  and  by  tie- 
plates  and  lattice  bars  at  the  bottom.  Gusset  plates  for  the 
connection  of  web  members  to  chords  shall  be  riveted  to 
the  inside  of  the  chords,  and  shall  be  designed  to  resist  the 
forces  to  which  they  are  subjected. 

136.  Web  Members. — Web  members  shall  intersect 
each  other  and  the  chords  on  lines  passing  through-  their 
centers  of  gravity,  and  shall  be  thoroughly  riveted  to  each 
other  and  to  the  connection  plates  at  every  intersection. 
Web  members  shall  be  composed  of  symmetrical  sections, 
connected  by  web-plates  or  tie-plates  and  lattice  bars.  The 
clear  distance  between  gussets  shall  be  not  more  than  i  inch 
greater  than  the  width  of  the  web  members  that  connect 
to  them. 

137.  Connections  and  Splices. — Splices  of  chords 
shall  be  as  close  as  practicable  to  panel  points.  All  splices 
of  chords  and  connections  of  web  members  shall  have  enough 
rivets  to  develop  fully  the  strength  of  the  members.  If  a 
splice  occurs  at  a  joint,  that  part  of  the  gusset  in  contact  with 
the  chord  shall  be  counted  as  a  splice  plate. 


38 


BRIDGE  SPECIFICATIONS 


74 


138.  Tension  Members. — Tension  members  shall  be 
of  the  same  general  form  as  compression  members.  The 
use  of  flat  bars  alone  for  riveted  tension  members  will  not 
be  allowed. 


DETAILS  OF  PIN-CONNECTED  TRUSSES 

139.  Chord  Members. — The  top  chord  and  end  posts 
shall  be  composed  of  channels,  or  of  vertical  plates  with 
flange  angles,  connected  by  cover-plates  at  the  top,  and  by 
tie-plates  and  lattice  bars  at  the  bottom,  or  by  tie-plates  and 
lattice  bars  at  both  top  and  bottom.  Splices  of  top  chords 
shall  be  as  close  as  practicable  to  panel  points,  and  shall  have 
enough  rivets  to  develop  fully  the  stresses  in  the  members. 
The  bottom  chord  shall  be  composed  of  eyebars;  the  inside 
bars  in  the  two  end  panels  shall  be  connected  to  each  other 
by  diaphragms  or  by  lattice  bars.  The  eyebars  shall  be 
packed  on  the  pins  as  narrow  as  possible;  those  in  any  panel 
shall  not  be  in  contact,  and  shall  not  diverge  from  the  center 
line  by  more  than  Te  inch  per  foot. 

140.  Web  Members. — Web  members  shall  intersect 
each  other  and  the  chords  on  lines  passing  through  their 
centers  of  gravity,  and  pins  shall  be  located  at  the  inter¬ 
sections  of  these  lines.  Compression  web  members  shall  be 
composed  of  symmetrical  sections,  connected  by  web-plates 
or  by  tie-plates  and  lattice  bars.  Tension  web  members, 
except  hip  verticals  and  subverticals,  shall  be  composed  of 
eyebars.  Hip  verticals  and  subverticals  shall  be  of  the  same 
general  form  as  compression  members. 

141.  Counters. — Counters  shall  be  adjustable  eyebars 
with  screw  ends  and  open  turnbuckles.  The  area  at  the  root 
of  an  upset  screw  end  shall  in  no  case  be  less  than  10  per 
cent,  greater  than  the  cross-sectional  area  of  the  body  of 
the  bar.  No  counter  shall  have  a  sectional  area  of  less 
than  2  square  inches. 

142.  Pins. — Pins  shall  be  not  less  than  2i  inches  in 
diameter,  and  shall  project  i  inch  at  each  end  beyond  the 
outside  surfaces  of  the  members. 


§74 


BRIDGE  SPECIFICATIONS 


39 


143.  Riveted  Tension  Members. — Riveted  tension 
members  shall  have  a  net  section  back  of  the  pinholes  equal 
to  that  of  the  member,  and  through  the  pinholes  25  per  cent, 
greater. 

144.  Pin  Plates. — Where  necessary  for  section  or 
bearing,  members  shall  be  reinforced  at  pinholes  by  pin- 
plates.  Each  plate  shall  contain  sufficient  rivets  to  transmit 
its  proportion  of  the  bearing  pressure  to  the  members;  one 
plate  on  each  side  shall  extend  at  least  6  inches  beyond  the 
end  of  the  tie-plate.  The  cross-section  of  a  compression 
member  through  the  pinhole  shall  be  equal  to  that  of  the 
member. 


DETAILS  OF  STEEL  TRESTLES 

145.  Tower  and  Main  Spans.— Steel  trestles  shall 
consist  of  riveted  spans  on  trestle  bents,  braced  in  pairs  to 
form  towers.  Tower  spans  shall  be  not  less  than  30  feet 
long,  and  shall  be  riveted  to  the  tops  of  the  trestle  bents. 
Main  spans  shall  be  riveted  to  the  tops  of  the  trestle  bents  at 
one  end,  and  bolted  to  them  at  the  other  through  expansion 
holes.  Girders  and  trusses  may  be  connected  to  the  tops  of 
the  columns  or  to  cross-girders  that  are  connected  to  the  tops 
of  the  columns. 

146.  Trestle  Bents. — The  batter  of  columns  in  trestle 
bents  shall  be  not  less  than  1  horizontal  to  8  vertical.  In 
trestles  for  single-track  railway  only,  bents  shall  be  not  less 
than  8  feet  wide  on  top,  and  'if  the  width  is  less  than  10  feet, 
the  batter  of  the  columns  shall  be  not  less  than  1  horizontal 
to  6  vertical.  On  curves,  towers  shall  be  placed  so  that  the 
center  lines  of  the  bents  are  at  right  angles  to  the  chord  of 
the  curve  between  the  bents. 

147.  Towers. — Towers  shall  be  divided  into  stories 
not  more  than  30  feet  in  height,  by  horizontal  struts  and 
diagonal  bracing  between  the  columns. 

148.  Negative  (Downward)  Reactions.  —  In  esti¬ 
mating  negative  (downward)  reaction's  at  the  feet  of  the 


40 


BRIDGE  SPECIFICATIONS 


74 


columns,  wind  pressure  shall  be  assumed  to  have  an  intensity 
of  50  pounds  per  square  foot,  acting  on  an  area  equal  to 
twice  the  exposed  area  of  the  unloaded  trestle. 


DETAILS  OF  BEARINGS 

149.  Bedplates. — The  ends  of  all  spans,  and  the 
bottoms  of  columns  of  trestle  bents,  shall  rest  on  bedplates 
or  pedestals,  and  shall  be  held  in  place  by  anchor  bolts. 
Bedplates  for  girders  and  stringers  shall  be  not  less  than 
i  inch  in  thickness;  and  for  trusses  and  columns,  not  less 
than  1  inch.  Holes  for  anchor  bolts  may  be  \  inch  larger  in 
diameter  than  the  bolts. 

150.  Anchor  Bolts. — Anchor  bolts  shall  be  not  less 
than  1  inch  in  diameter;  they  shall  be  set  in  holes  drilled  in 
the  masonry,  and  the  holes  shall  be  filled  with  cement  grout. 
Anchor  bolts  for  columns  having  negative  reactions  shall  be 
designed  to  resist  the  reaction,  and  shall  be  built  in  a  mass 
of  masonry  the  weight  of  which  is  not  less  than  twice  the 
estimated  reaction.  Anchor  bolts  in  expansion  ends  shall  be 
so  placed  that  the  ends  can  move  freely  in  the  direction  of 
expansion  and  in  no  other  direction. 

151.  Pedestals. — Spans  over  75  feet  in  length  shall 
have  pin  bearings  and  pedestals  at  both  ends.  Pedestals 
shall  preferably  be  built  up  of  base  plates  and  web-plates, 
not  less  than  f  inch  in  thickness.  The  webs  shall  be  secured 
to  the  base  plates  by  angles  not  less  than  5  in.  X  3i  in.  X  i  in., 
with  the  5-inch  leg  vertical,  and  the  webs  shall  be  connected 
to  each  other.  Pedestals  shall  be  of  sufficient  height  to  dis¬ 
tribute  the  load  over  the  bearings. 

152.  Ends  of  Columns. — Cap  and  base  plates  shall  be 
connected  to  the  tops  and  bottoms,  respectively,  of  all  trestle 
columns  by  means  of  horizontal  angles  not  less  than 
5  in.  X  3i  in.  X  2  in.,  with  the  5-inch  leg  vertical  or  parallel 
to  the  batter  of  the  column. 

153.  Rollers. — Spans  over  75  feet  in  length  shall  have 
rollers  at  one  end.  Rollers  shall  be  not  less  than  3  inches 


74 


BRIDGE  SPECIFICATIONS 


41 


in  diameter,  and  shall  be  turned  down  to  a  groove  i  inch 
deep  to  fit  guiding  strips  of  this  thickness  on  the  bearing 
plates  above  and  below  the  rollers.  Special  attention  shall 
be  given  to  roller  bearings,  so  that  they  will  not  hold  water 
and  so  that  they  can  be  readily  cleaned. 


DETAILS  OF  BRACING 

154.  All  spans  shall  be  independently  braced;  no  bra¬ 
cing  shall  be  used  in  common  for  any  two  adjacent  spans. 

155.  Style  of  Members. — Members  of  bracing  shall 
be  composed  of  simple  rolled  sections  or  built-up  members. 
No  member  shall  be  less  than  2i  in.  X  2i  in.  X  iis  in.,  and 
no  connection  shall  have  less  than  three  rivets. 

156.  Lateral  Bracing. — Top  and  bottom  lateral  bra¬ 
cing  shall  be  provided  in  all  deck  and  through  bridges,  except 
deck  plate  girders  less  than  5  feet  deep,  where  the  bottom 
bracing  may  be  omitted.  Bottom  lateral  bracing  shall  be 
provided  in  half-through  bridges.  Lateral  bracing  shall  be 
riveted  to  the  stringers  of  the  floor  system  wherever  they 
come  in  contact  with  them.  Deck  girders  shall  have  the  top 
lateral  bracing  so  arranged  that  the  length  of  flange  between 
lateral  connections  will  not  exceed  twenty  times  the  width  of 
flange. 

157.  Transverse  Bracing. — Deck  girder  bridges  shall 
have  transverse  frames  of  the  same  depth  as  the  girders 
riveted  to  the  stiffeners  near  the  ends  and  at  other  points  at 
distances  apart  not  greater  than  20  feet.  Deck  truss  bridges 
shall  have  at  every  panel  point  sway-bracing  of  the  same 
depth  as  the  trusses. 

158.  Knee  Bracing.- — Half-through  bridges  shall  have 
brackets  or  knee  braces  riveted  to  the  floorbeams  and  to  the 
webs  of  the  girders.  The  brackets  shall  fit  tight  under  the 
flange  angles  of  the  girders,  and  extend  out  to  within  3  inches 
of  the  edge  of  the  wheel-guard. 

159.  Portal  Bracing. — Through  bridges  shall  have 
portals  and  portal  brackets,  and  intermediate  brackets  at 


42 


74 


BRIDGE  SPECIFICATIONS 

i 

each  transverse  strut  of  the  upper  lateral  bracing.  Portals 
shall  be  as  deep  as  the  specified  headroom  will  allow.  Where 
the  headroom  above  the  floor  is  20  feet  or  more,  sway  frames 
shall  be  provided  at  every  panel  point  of  the  top  chord.  They 
shall  be  as  deep  as  the  required  headroom  will  allow. 


SPECIFICATIONS  FOR  THE  CONSTRUC¬ 
TION  OF  STEEL  BRIDGES 


MATERIALS 


CHEMICAL  AND  PHYSICAL  PROPERTIES 

160.  Kind  of  Material. — The  materials  used  in  the 
construction  of  bridges  shall  generally  be  rolled  steel,  steel 
castings,  and  wrought  iron.  In  case  other  materials  are 
required,  additional  specifications  will  be  furnished  relating 
to  them. 

161.  Grades  of  Steel. — Steel  shall  be  made  only  by 
the  open-hearth  process.  Rolled  steel  shall  be  of  two 
grades;  namely,  rivet  steel  and  structm'al  steel.  Rivet  steel 
shall  be  used  for  rivets;  structural  steel  shall  be  used  for  all 
other  purposes,  unless  steel  castings  or  wrought  iron  fire 
especially  called,  for. 

162.  Rivet  Steel. — Rivet  steel  shall  contain  not  more 
than  .04  per  cent,  of  phosphorus,  nor  more  than  .04  per  cent, 
of  sulphur.  It  shall  have  an  ultimate  tensile  strength  of  not 
less  than  46,000,  nor  more  than  54,000,  pounds  per  square 
inch,  an  elastic  limit  of  not  less  than  60  per  cent,  of  the  ulti¬ 
mate  strength,  an  elongation  of  not  less  than  28  per  cent., 
including  the  break,  and  a  reduction  of  area  of  not  less  than 
55  per  cent.  Rivet  rods  shall  bend  double,  cold,  one  side 
flat  on  the  other,  without  cracking  of  the  outer  fibers. 

163.  Structural  Steel. — Structural  steel  shall  contain 
not  more  than  .08  per  cent,  of  phosphorus  for  acid  steel, 
nor  more  than  .04  for  basic  steel,  and  not  more  than  .04  per 


§74 


BRIDGE  SPECIFICATIONS 


43 


cent,  of  sulphur  for  either  kind  of  steel.  It  shall  have  an 
ultimate  tensile  strength  of  not  less  than  56,000,  nor  more 
than  64,000,  pounds  per  square  inch,  an  elastic  limit  of  not 
less  than  60  per  cent,  of  the  ultimate  strength,  an  elongation 
of  not  less  than  28  per  cent.,  and  a  reduction  of  area  at 
fracture  of  not  less  than  50  per  cent.  The  fracture  shall 
appear  fine-grained,  silky,  and  bluish  gray,  and  shall  be 
entirely  free  from  hard  and  granular  spots. 

Test  pieces  shall  bend  double,  cold,  until  the  surfaces 
touch  each  other,  without  cracking  of  the  outer  fibers. 
They  shall  stand  punching  and  cold  reaming  to  li  times 
the  diameter  of  the  punched  hole  without  cracking  the  edges 
of  the  hole.  Angles  of  all  thicknesses  shall,  while  cold, 
open  flat,  and  if  under  f  inch  thick  shall  bend  close  shut 
without  showing  signs  of  fracture. 

164.  Steel  Castings. — Steel  castings  shall  contain  not 
more  than  .08  per  cent,  of  phosphorus  for  acid  steel,  nor 
more  than  .05  per  cent,  for  basic  steel,  nor  more  than  .05  per 
cent,  of  sulphur  for  either  kind  of  steel.  They  shall  have  an 
ultimate  tensile  strength  of  not  less  than  60,000  pounds  per 
square  inch,  an  elastic  limit  of  not  less  than  60  per  cent,  of 
the  ultimate  strength,  an  elongation  of  not  less  than  18  per 
cent.,  and  a  reduction  of  area  at  fracture  of  not  less  than 
25  per  cent.  Steel  castings  shall  be  fine-grained,  homoge¬ 
neous,  and  free  from  blowholes  and  other  defects.  A  test 
piece  1  in.  X  2  in.  shall  bend  cold  through  an  angle  of  90° 
around  a  rod  whose  diameter  is  li  inches,  without  showing 
signs  of  fracture. 

165.  Wrought  Iron. — Wrought  iron  shall  be,  as  nearly 
as  practicable,  the  best  grade  of  pure  iron.  It  shall  be 
double-rolled,  fibrous,  tough,  uniform  in  character,  and 
thoroughly  welded  in  rolling.  It  shall  be  entirely  free  from 
surface  defects.  It  shall  have  an  ultimate  tensile  strength 
of  not  less  thg.n  50,000  pounds  per  square  inch,  an  elastic 
limit  of  not  less  than  60  per  cent,  of  the  ultimate  strength, 
an  elongation,  including  the  break,  of  not  less  than  18  per 
cent.,  and  a  reduction  of  area  at  fracture  of  not  less  than 


44 


BRIDGE  SPECIFICATIONS 


74 


25  per  cent.  Test  pieces  shall  bend,  when  cold,  through  an 
angle  of  180°  around  a  rod  whose  diameter  is  twice  the  thick¬ 
ness  of  the  test  piece,  without  showing  signs  of  fracture. 


MILL.  TESTS 

166.  Reports  of  Tests  and  Melt  Numbers. — The 
Contractor  shall  furnish  the  Engineer,  free  of  charge,  a  report 
showing  the  physical  and  chemical  properties  of  every  melt 
that  goes  into  the  material  of  the  bridge.  The  chemical 
analysis  shall  show  the  amount  of  carbon,  phosphorus,  sul¬ 
phur,  and  manganese  contained  in  each  melt.  The  melt 
numbers  shall  be  clearly  stamped  on  all  finished  material, 
and  omission  to  do  so,  or  changes,  or  confusion  of  the  melt 
numbers  may  be  cause  for  rejection. 


167.  Test  Pieces. — Two  test  pieces  shall  be  cut  from 
the  finished  material  of  every  melt.  Test  pieces  of  rivet 

steel  shall  be  round 
rods  having  the  same 
diameter  as  the 
rivets.  Test  pieces 
of  structural  steel  for 
pins  and  rollers  shall 
be  round  rods  turned 
to  the  form  and  size  shown  in  Fig.  8.  The  elongation  shall 
be  measured  in  a  length  of  2  inches,  and  include  the  break. 

Test  pieces  of  structural  steel  for  other  purposes,  and  of 
wrought  iron,  shall  be  flat  bars  of  the  same  thickness  as  the 
material  from  which  the  test  pieces  are  cut,  and  shall  have 


Fig.  9 


the  form  and  size  shown  in  Fig.  9.  The  elongation  shall  be 
measured. in  a  length  of  8  inches,  including  the  break. 

Test  pieces  of  steel  castings  shall  be  cast  with  one  or 
more  castings,  and  shall  be  cut  from  them  when  they  are 


BRIDGE  SPECIFICATIONS 


45 


§74 

cold;  they  shall  be  turned  to  the  form  and  size  shown  in 
Fig.  8,  and  the  elongation  shall  be  measured  in  a  length 
of  2  inches,  including  the  break. 

168.  Annealed  Material. — Two  test  pieces  shall  be 
cut  from  material  that  is  to  be  annealed,  one  before  and  the 
other  after  annealing. 

169.  Varying  Sections. — Test  pieces  shall  be  cut 
from  the  thickest  and  from  the  thinnest  materials  when 
sections  differing  by  f  inch  or  more  are  rolled  from  the  same 
melt,  and  from  each  section  when  widely  different  sections, 

such  as  angles  and  I  beams,  are  rolled  from  the  same  melt. 

% 

170.  Labor  and  Tools. — The  Contractor  shall  furnish 
the  Engineer,  free  of  charge,  proper  test  pieces,  machines, 
tools,  and  labor  necessary  to  make  the  required  tests. 

171.  Rejection  of  Materials. — If  material  does  not 
possess  the  specified  properties,  the  entire  melt  from  which 
the  material  was  taken  shall  be  rejected,  unless  by  additional 
tests  it  can  be  proved  that  the  defects  are  confined  to  only  a 
part  of  the  melt.  All  material  that,  subsequently  to  its 
acceptance  at  the  mills,  shows  that  it  is  not  of  the  desired 
quality  shall  be  rejected  and  shall  be  replaced  with  satis¬ 
factory  material.  Rusty  material  shall  be  rejected,  unless 
it  is  thoroughly  freed  from  rust  before  being  used. 


FULL-SIZE  TESTS 

172.  Full-sized  members  shall  be  tested  to  destruction 
if  so  directed  by  the  Engineer.  The  material  in  such 
members  shall  be  paid  for  by  the  Engineer  at  the  contract 
price  per  pound,  if  it  complies  with  the  requirements;  other¬ 
wise,  it  will  be  rejected  at  the  Contractor’s  expense,  and  all 
similar  members  may  be  rejected  unless  it  can  be  shown, 
by  additional  tests,  that  the  failure  is  due  to  defects  that  are 
confined  to  one  or  a  very  few  members. 

173.  Eyebar  Tests. — In  general,  one  full-size  test  shall 
be  made  from  every  twenty-five  eyebars.  After  being 


46 


BRIDGE  SPECIFICATIONS 


§74 


properly  annealed,  eyebars  shall  have  an  ultimate  tensile 
strength  of  not  less  than  55,000  pounds  per  square  inch,  an 
elastic  limit  of  not  less  than  50  per  cent,  of  the  ultimate 
strength,  and  an  elongation  of  not  less  than  15  per  cent,  in 
10  feet,  including  the  break.  If  a  bar  breaks  in  the  head,  but 
develops  the  required  ultimate  strength  and  elongation,  it 
shall  not  on  that  account  be  rejected,  unless  more  than  one- 
third  of  the  number  of  bars  tested  break  in  the  head. 


WORKMANSHIP 


GENERAL  REQUIREMENTS 

174.  Finished  Material. — Workmanship  and  finish 
shall  be  first-class  and  in  accordance  with  the  best  practice. 
Material  shall  get  a  thorough  rolling  at  the  proper  tem¬ 
perature;  large  sections  shall  be  rolled  from  large-sized 
billets;  pins  shall  be  forged  in  the  most  approved  manner. 
Finished  material  shall  be  entirely  free  from  surface  defects, 
shall  have  good  finish,  and  be  well  straightened  in  the  mill 
before  shipment. 

175.  Variation  in' Dimensions. — Material  shall  be 
rolled  as  near  as  practicable  to  the  weight  and  thickness 
specified;  no  variation  will  be  allowed  greater  than  2i  per 
cent,  above  nor  li  per  cent,  below  the  computed  weights, 
except  in  wide-sheared  plates,  for  which  slightly  greater 
variation  will  be  allowed,  according  to  the  practice  in  the 
best  rolling  mills. 

176.  Annealing. — All  parts  that  have  been  heated  dur¬ 
ing  manufacture  shall  be  carefully  annealed  and  thoroughly 
cooled  before  they  are  prepared  for  connections. 

177.  Welding. — Welds  in  steel  will  not  be  allowed 
under  any  circumstances.  Welds  in  wrought  iron  will  be 
permitted  when  specified. 

178.  Reentrant  Angles. — No  sharp  reentrant  angles 
will  be  allowed  in  any  piece  of  metal;  the  corners  shall  always 
be  drilled  out  before  the  sides  are  cut. 


§74 


BRIDGE  SPECIFICATIONS 


47 


179.  Rivet  Holes.- -Rivet  holes  in  members  of  longitu¬ 
dinal  and  lateral  bracing,  stiffeners,  and  unimportant  details 
may  be  punched  not  more  than  ft  inch  larger  than  the 
nominal  diameter  of  the  rivets.  Rivet  holes  in  flanges,  the 
edges  of  web-plates  where  flanges  are  attached,  floor  connec¬ 
tions,  and  all  riveted  members  of  trusses  and  their  connections 
shall  be  punched  -ft  inch  smaller,  and  reamed  to  not  more 
than  ft  inch  larger  than  the  nominal  diameter  of  the  rivets,  if 
the  material  is  ft  inch  thick  or  less.  Reaming  shall  prefer¬ 
ably  be  done  after  the  parts  are  assembled.  Rivet  holes  in 
material  f  inch  thick  and  over,  and  in  flanges  of  I  beams  and 
channels,  shall  be  drilled  from  the  solid  metal. 

180.  Punching. — Rivet  holes  shall  be  spaced  and 
punched  so  accurately  that,  when  parts  are  brought  together, 
the  corresponding  holes  will  match.  Slight  inaccuracies  may 
be  corrected  by  reamers.  Drifting  to  make  holes  large  enough 
for  the  rivets  will  not  be  allowed  in  the  shop  or  in  the  field. 

181.  Reaming  and  Drilling. — When  parts  are  assem¬ 
bled  for  reaming,  at  least  one-third  of  the  holes  shall  be  filled 
with  bolts.  If  necessary  to  take  them  apart  for  shipment, 
they  shall  be  match-marked,  and  a  diagram  of  the  marks 
shall  be  furnished  the  erector  to  insure  the  same  position 
of  each  part  in  the  finished  bridge  as  in  the  shop.  Parts 
assembled  for  drilling  shall  be  taken  apart,  and  any  shavings 
between  them  removed  before  riveting.  Burrs  on  reamed 
and  drilled  work  shall  be  removed. 

.  i 

182.  Field  Connections. — All  field  connections,  except 
for  members  of  bracing,  shall  be  fitted  in  the  shop.  The 
rivet  holes  shall  be  reamed  to  fit  while  the  members  are 
bolted  together  in  their  correct  positions,  or  by  means  of 
metal  templets  not  less  than  li  inches  thick,  carefully 
clamped  to  the  members  in  the  correct  position. 

183.  Rivets. — The  sizes  of  rivets  shown  on  the  plans 
shall  be  taken  to  mean  the  diameters  of  the  cold  rivets 
before  driving.  When  heated  and  ready  for  driving,  the  sur¬ 
faces  of  all  rivets  shall  be  perfectly  clean;  when  driven,  they 


48 


BRIDGE  SPECIFICATIONS 


§74 

shall  completely  fill  the  holes  and  be  perfectly  tight.  Loose 
and  badly  driven  rivets  shall  be  cut  out  and  replaced  with 
tight  well-driven  rivets.  Rivet  heads  shall  be  round  and  of 
uniform  size  for  the  same-sized  rivets  all  through  the  work; 
they  shall  be  full  and  neatly  made,  concentric  with  the 
shank,  and  in  full  contact  with  the  surface. 

184.  Riveting. — Wherever  possible,  rivets  shall  be 
driven  by  machine  or  power  riveters.  Power  riveters  shall 
be  capable  of  maintaining  the  applied  pressure  after  driving. 
Field  riveting  shall  preferably  be  done  by  pneumatic  riveting 
hammers.  Before  any  rivets  are  driven,  at  least  one-third 
the  holes  shall  be  filled  with  bolts  of  the  same  size  as  the 
rivets,  and  they  shall  be  carefully  tightened. 

185.  Bolts. — Bolts  shall  not  be  used  in  place  of  rivets, 
except  by  special  permission.  When  bolts  are  used,  the  holes 
shall  be  exactly  at  right  angles  to  the  surfaces  of  the  con¬ 
nected  parts,  and  the  bolts  shall  be  turned  to  a  driving  fit. 

186.  Riveted  Members. — After  being  riveted,  mem¬ 
bers  shall  be  straight  and  correct  in  dimensions.  Great  care 
shall  be  taken  that  the  bearing  surfaces  of  girders  and  the 
faces  of  flange  angles  of  girders  and  riveted  truss  members 
are  perfectly  straight. 

187.  Web-Plates. — Web-plates  shall  be  straight  and 
not  project  beyond  the  faces  of  the  flange  angles;  they  shall 
be  not  more  than  i  inch  below  the  faces  of  the  angles  at  any 
point.  Splices  in  web-plates  shall  be  not  more  than  i  inch 
open. 

188.  Flange  Members. — Where  flange  members  of 
plate  girders  are  spliced,  in  either  the  top  or  the  bottom 
flange,  the  ends  shall  be  planed  exactly  square;  and,  after 
riveting,  the  spliced  ends  shall  be  in  perfect  contact  through¬ 
out  the  entire  section  of  the  spliced  member. 

189.  Stiffeners. — Stiffeners  shall  fit  tight  between  the 
horizontal  legs  of  flange  angles;  the  ends  of  fillers  under 
stiffeners,  and  of  web  splice  plates  shall  be  not  more  than 

inch  from  the  edges  of  the  vertical  legs  of  the  flange  angles. 


BRIDGE  SPECIFICATIONS 


49 


§T4 

190.  Ends  of  Floor  Members. — The  ends  of  floor- 
beams  and  stringers  shall  be  planed  perfectly  smooth  and 
straight;  after  planing,  the  members  shall  have  the  length 
shown  on  the  plans.  Not  more  than  iV  inch  shall  be  planed 
off  the  faces  of  the  connection  angles.  Ends  of  solid  floor 
sections  shall  be  perfectly  straight  and  smooth;  if  necessary, 
they  shall  be  planed  to  secure  this  result. 

191.  Ends  of  Riveted  Members. — Where  riveted 
members,  either  tension  or  compression,  are  spliced,  the 
ends  shall  be  planed  smooth  exactly  at  right  angles  to  the 
axis  of  the  member;  and,  after  riveting,  the  spliced  ends 
shall  be  in  perfect  contact  throughout  the  entire  section  of 
the  spliced  member.  The  ends  of  columns  of  viaducts  shall 
be  planed  smooth  before  the  cap  and  base  plates  are  riveted 
on,  and  so  that  the  entire  section  of  the  column,  as  well  as 
the  faces  of  the  horizontal  angles  riveted  to  the  ends,  shall 
have  a  full  and  even  bearing  on  the  cap  and  base  plates. 

192.  Ends  of  Girders. — The  ends  of  all  girders  shall 
be  neatly  finished;  web-plates,  flange  angles,  and  flange  plates 
shall  be  finished  flush  with  each  other. 

193.  Eyebars. — Eyebars  shall  be  of  uniform  thickness 
throughout,  perfectly  straight,  and  free  from  welds.  The 
heads  shall  be  full,  smooth,  and  sound,  and  accurately 
centered  with  the  bars;  they  shall  be  formed  by  upsetting 
in  the  most  approved  manner.  After  the  heads  are  formed, 
eyebars  shall  be  carefully  annealed  and  thoroughly  cooled 
before  further  handling. 

194.  Pinboles.  —Pinholes  shall  be  bored  exactly  at 
right  angles  to  the  axis  of  the  member,  not  more  than 
5V  inch  larger  in  diameter  than  the  pins  up  to  5  inches 
diameter,  nor  more  than  ih  inch  larger  for  diameters  greater 
than  5  inches,  and  not  more  than  -&t  inch  greater  or  less  than 
the  calculated  distance  center  to  center  as  shown  on  the 
drawings.  The  centers  of  pinholes  in  riveted  members  shall 
generally  lie  on  a  line  passing  through  the  center  of  gravity 

of  the  member,  unless  shown  elsewhere  on  the  drawings. 

135—5 


50 


BRIDGE  SPECIFICATIONS 


§74 


The  centers  of  pinholes  in  eyebars  shall  be  on  the  center 
line.  Bars  that  are  to  be  placed  side  by  side  in  a  bridge 
shall  be  bored  so  accurately  that,  if  stacked  up  one  above 
the  other,  a  pin  of  the  required  size  can  be  passed  simul¬ 
taneously  through  all  the  holes  at  either  end  without  much 
forcing. 

195.  Pins. — Pins  shall  be  forged  and  carefully  turned 
cylindrical,  smooth,  and  true  to  size,  and  long  enough  to  give 
all  members  a  full  bearing.  They  shall  be  driven  with  pilot 
nuts  and  caps;  at  least  one  driving  cap  and  pilot  nut  for  each 
size  of  pin  shall  be  furnished  by  the  Contractor.  Threads  on 
ends  of  pins  shall  project  \  inch  beyond  the  surfaces  of  the 
nuts  when  they  are  screwed  on. 

196.  Pin  Nuts. — Pin  nuts  shall  be  made  so  as  to 
enclose  the  projecting  ends  of  pins  and  come  to  a  full 
bearing  against  the  members. 

197.  Rollers. — Rollers  shall  be  forged  and  carefully 
turned  cylindrical,  smooth,  and  true  to  size. 

198.  Bearings. — Sole  plates  and  bedplates  shall  be 
planed  smooth  and  straight.  The  sliding  surfaces  at  expan¬ 
sion  ends  shall  be  planed  in  the  direction  of  expansion.  The 
bottoms  of  webs  and  connection  angles  of  pedestals  shall  be 
planed  before  the  base  plates  are  riveted  on. 

199.  Steel  Castings. — Steel  castings  shall  be  planed 
where  noted  on  drawings  and  wherever  else  it  is  necessary 
to  insure  good  workmanship  and  even  bearing.  Cored  holes 
shall  be  not  more  than  s  inch  greater  or  less  than  the  required 
sizes,  nor  more  than  i  inch  from  the  position  shown  on  the 
drawings.  Steel  castings  shall  be  true  to  the  required 
dimensions  after  annealing. 

200.  Shipment. — All  pins,  rivets,  and  other  small  parts 
shall  be  boxed,  and  the  screw  threads  wrapped  with  twine, 
before  shipment.  An  excess  of  field  rivets  equal  to  20  per 
cent,  of  the  required  number  for  each  size  and  length  shall  be 
shipped  for  each  bridge.  All  members  shall  be  handled  and 
loaded  on  cars  in  such  a  way  as  to  avoid  injury;  any  piece 


74 


BRIDGE  SPECIFICATIONS 


51 


showing  the  effects  of  rough  handling  may  be  rejected.  The 
weight  and  erection  mark  shall  be  plainly  marked  on  each 
part,  and  the  weight  and  contents  on  each  box. 


PAINTING 

201.  General. — As  soon  as  material  is  finished  and 
accepted,  it  shall  be  thoroughly  cleared  of  rust,  dirt,  scale, 
and  other  surface  deposits,  and  carefully  painted  in  accord¬ 
ance  with  the  following  specifications.  No  painting  shall 
be  done  until  material  is  accepted. 

202.  Surfaces  in  Contact. — Surfaces  that  will  be  in 
contact  with  others  shall  be  given  one  coat  of  red  lead  and 
linseed  oil  before  assembling. 

203.  Inaccessible  Parts. — All  parts  not  accessible 
for  painting  after  erection  shall  be  given  one  heavy  coat  of 
approved  paint  at  the  shop  as  soon  as  finished  and  accepted, 
and  one  coat  at  the  bridge  site  before  erection. 

204.  Machined  Surfaces. — All  machined  surfaces,  such 
as  screw  threads,  pins,  and  bearing  surfaces  shall  be  coated 
with  a  mixture  of  white  lead  and  tallow  as  soon  as  finished 
and  before  leaving  the  shop. 

205.  Finished  Members. — Finished  members  shall  be 
given  one  heavy  coat  ‘of  approved  paint  before  leaving  the 
shop.  In  general,  paint  shall  be  allowed  to  dry  48  hours 
before  loading  material  for  shipment. 

206.  Painting  After  Erection. — After  erection,  the 
bridge  shall  be  given  two  heavy  coats  of  approved  paint.  At 
least  48  hours  must  elapse  between  the  applications  of  the 
two  successive  coats  to  any  part  of  the  bridge. 

207.  Weather  Conditions. — Painting  shall  be  done 
only  when  the  surface  of  the  metal  is  perfectly  dry.  Field 
painting  shall  not  be  done  in  wet  or  freezing  weather.  Shop 
painting  may  be  done  in  such  weather,  if,  after  painting,  the 
material  is  allowed  to  remain  at  least  48  hours  in  a  covered 
building  whose  inside  temperature  is  not  below  freezing. 


BRIDGE  SPECIFICATIONS 


§74 


208.  Quality. — The  quality  of  paint  and  class  of  labor 
for  painting  shall  be  the  best  obtainable;  special  attention 
shall  be  given  to  this  part  of  the  work. 


ERECTION 

209.  Commencement  of  Work. — The  Contractor  shall 
notify  the  Engineer  when  he  is  ready  to  commence  work,  and 
the  erection  shall  not  begin  until  authority  has  been  received 
in  writing  from  the  Engineer. 

210.  Care  of  Material. — Before  and  during  erection, 
all  material  shall  be  kept  clean  and  so  stored  and  handled  as 
to  avoid  injury. 

211.  Old  Structures. — If  the  new  bridge  is  to  take 
the  place  of  an  old  bridge  on  the  same  site,  the  Contractor 
shall  take  down  the  old  bridge;  if  required,  he  shall  take  it 
down  without  loss  or  injury  to  any  part,  and  shall  mark  all 
parts  for  reerection.  A  diagram  showing  these  marks  shall 
be  furnished  to  the  Engineer. 

212.  Method  of  Erection. — If  it  is  necessary  to  place 
any  restrictions  on  the  method  of  erection,  the  Engineer  shall 
state  them  in  the  letter  of  invitation  to  bid;  he  shall  also 
state  the  desired  disposal  of  the  old  bridge. 

213.  Eines  and  Grades. — The  Contractor  will  be 
expected  to  preserve  with  care  all  stakes  set  by  the  Engineer. 

214.  Field  Riveting  in  Splices. — Field  rivets  in 
splices  of  compression  members  shall  not  be  driven  until  the 
members  are  subjected  to  dead-load  stress.  The  splices  shall 
be  well  bolted  prior  to  this,  to  hold  the  members  firmly  in  line. 

215.  Bridge  Seats. — Bridge  seats  shall  be  dressed 
by  the  Contractor.  If  they  are  out  of  level,  he  shall  place  the 
bedplates  or  pedestals  level  and  at  the  correct  elevation;  if 
necessary,  he  shall  fill  in  under  them  with  cement  grout  well 
rammed  into  all  open  spaces  under  the  bedplates  or  pedestals. 
The  grout  shall  be  allowed  to  set  at  least  24  hours  before  any 
load  is  placed  on  the  bedplate  or  pedestal. 


§74 


BRIDGE  SPECIFICATIONS 


53 


216.  Laws  and  Ordinances.— The  Contractor  shall 
comply  with  all  laws  and  ordinances  applying  to  and  gov¬ 
erning  the  work  of  erection,  and  shall  obtain  all  necessary 
permits  and  comply  with  their  requirements.  He  shall  take 
precautions  to  guard  against  accidents  and  injury  to  persons 
and  property,  and  shall  be  responsible  for  all  losses  due  to 
floods,  storms,  and  other  casualties.  He  shall  so  conduct 
his  work  as  not  to  interfere  with  the  work  of  other  Contractors, 
nor  with  the  traffic  on  railroads,  highways,  or  waterways, 
unless  he  procures  written  permission  to  do  otherwise. 

217.  Extra  Work. — If  the  Engineer  erects  the  bridge 
and  extra  work  is  found  to  be  necessary  owing  to  defective 
shop  work  or  careless  handling,  the  Contractor  shall  bear  the 
cost  of  it;  this  cost  shall  be  deducted  from  the  amount  due  him. 

218.  Employment  of  Men. — The  Contractor  shall 
follow  all  reasonable  directions  of  the  Engineer  in  regard  to 
the  discipline  of  his  men  during  the  work  of  erection.  At  the 
completion  of  the  work  he  shall,  if  desired  by  the  Engineer, 
furnish  proper  bond  to  protect  the  Engineer  from  all  liabili¬ 
ties  resulting  from  the  failure  of  the  Contractor  to  pay  for 
the  materials  or  labor. 

219.  Final  Test.. — As  soon  as  the  bridge  is  completed 
and  before  its  final  acceptance,  the  Engineer  may  test  it  by 
loading  it  with  the  specified  loads.  Any  defect  that  becomes 
apparent  shall  be  corrected  by  the  Contractor. 

220.  Name  Plate. — A  name  plate  of  neat  design  and 

finish,  giving  the  name  of  the  Contractor  and  the  date  of  erec¬ 
tion,  shall  be  firmly  attached  to  each  bridge  in  a  prominent 
position.  _ 


INSPECTION 

221.  Inspectors. — All  material  shall  be  tested  by,  and 
all  workmanship  shall  be  under  the  supervision  of,  inspectors 
appointed  by  the  Engineer.  The  Engineer  and  his  inspectors 
shall  have  free  access  at  all  times  to  all  parts  of  the  mills  and 
shops  in  which  any  part  of  the  bridge  is  being  manufactured. 


54 


BRIDGE  SPECIFICATIONS 


74 


222.  Reports  of  Inspectors. — Inspectors  shall  report 
the  results  of  all  tests;  the}7  shall  report  the  shipments  of 
material  from  the  mills  to  the  shops,  and  check  the  shipments 
off  from  the  bills  of  material  as  fast  as  they  are  made.  They 
shall  also  report  the  progress  of  the  work,  and  in  their  final 
report  shall  state  if  the  work  as  a  whole  was  carried  out  in  a 
satisfactory  manner,  noting  any  errors  that  may  have  been 
made. 

223.  Mill  Orders  and  Sharping  Invoices. — When 
the  Contractor  places  the  orders  for  the  material,  he  shall 
at  the  same  time  inform  the  Engineer  as  to  the  order  num¬ 
bers,  the  furnace  where  the  ingots  are  cast,  and  the  mills 
where  the  material  is  rolled.  He  shall  also  send  two  com¬ 
plete  copies  of  the  mill  orders,  and  shall  arrange  to  have 
the  inspectors  furnished  with  complete  copies  of  shipping 
invoices  with  each  shipment. 

224.  Facilities  for  Testing. — The  Contractor  shall 
furnish,  free  of  charge,  all  facilities,  labor,  tools,  and  instru¬ 
ments  or  machines  necessary  for  inspection,  testing,  and 
weighing. 


GENERAL  REMARKS 

225.  Engineering  Work. — All  the  engineering  work 
in  connection  with  the  design  and  construction  of  bridges  is 
done  by  one  or  more  bridge  engineers  and  their  assistants 
in  the  employ  of  the  city,  town,  or  company  that  is  to 
build  the  bridge.  In  some  cases,  engineers  are  employed 
permanently,  such  as  city  engineers  and  chief  and  bridge 
engineers  of  railroad  companies;  in  other  cases,  they  are 
employed  temporarily,  and  only  for  the  purpose  of  designing 
and  superintending  the  construction  of  one  or  more  bridges. 

226.  Letter  of  Invitation. — Before  the  design  of  the 
bridge  is  begun,  certain  dimensions  and  conditions  must  be 
known.  These  can  be  tabulated  for  almost  all  bridges  in 
the  form  given  below,  the  blanks  being  filled  out  for  each 
bridge,  and  a  copy  furnished  the  designer.  In  some  cases, 


74 


BRIDGE  SPECIFICATIONS 


55 


GENERAL  DATA 

For  bridge  over _ 

at _ _ 

Length  and  general  dimensions _ 


Skew  or  angle  of  abutments  with  center  line  of  bridge 


Width  of  bridge  and  location  of  trusses 


Floor  system _ 

Number  and  location  of  tracks _ 

Loadin  g _ 

Description  of  abutments _ 

Distance  from  floor  to  clearance  line 

«(  <<  l<  <£  1  ♦  1 

high  water _ 

<(  <(  ((  «£  -I 

low  water _ 

(<  <(  <<  <c  i 

river  bottom_ 

Character  of  river  bottom _ 

Usual  season  for  floods _ 

Name  of  nearest  railroad  station _ 

Distance  to  nearest  railroad  station _ 

Time  limit _ 

Name  of  Engineer _ - _ 

Address  of  Engineer _ 

Remarks _ 


56 


BRIDGE  SPECIFICATIONS 


§  74 


a  copy  is  sent  to  the  bidder  with  the  letter  of  invitation,  and 
he  is  requested  to  submit  a  proposed  plan  with  his  bid.  In 
the  majority  of  cases,  however,  the  bidder  is  furnished  with 
a  plan  that  gives  all  the  information  called  for  on  the  blank 
form,  and  in  addition  the  stresses  in  the  members. 

227.  When  it  is  necessary  to  have  a  bridge  ready  for 
traffic  at  a  certain  date,  this  date  is  stated  in  the  letter  of 
invitation.  In  some  cases,  bidders  are  offered  a  bonus  for 
each  day  the  bridge  is  finished  before,  and  required  to  pay  a 
penalty  for  each  day  the  bridge  is  finished  after,  the  stated 
time. 

228.  Location. — The  first  step  in  the  design  of  a  bridge 
is  the  selection  of  a  site,  and  the  arrangement  of  spans  and 
location  of  piers  and  abutments.  No  fixed  rule  can  be  given 
for  the  location  of  the  bridge  and  abutments  or  piers;  these 
are  matters  that  depend  almost  wholly  on  local  conditions, 
and  must  be  decided  by  the  judgment  of  the  engineer.  In 
general,  however,  it  may  be  said  that  the  site  should  be 
chosen  with  regard  to  economy  and  so  that  the  bridge  will 
be  in  a  good  position  to  accommodate  the  traffic.  As  a  rule, 
single  spans  are  most  economical  for  short  bridges,  and  steel 
trestles  for  long  bridges.  If  the  bridge  is  over  a  river,  and 
a  steel  trestle  cannot  be  used,  owing  to  the  danger  from 
floods  or  because  the  piers  would  block  navigation,  the 
bridge  may  be  composed  of  two  or  more  spans  resting  on 
masonry  piers;  or,  if  at  a  great  elevation  above  the  river,  so 
that  high  piers  are  expensive  and  objectionable,  a  single 
long  span  may  be  used.  It  is  frequently  necessary  to  esti¬ 
mate  the  approximate  cost  of  several  plans  and  designs 
before  one  is  finally  selected. 

229.  Kind  of  Bridge. — When  the  location  of  the  piers 
has  been  decided,  the  number  and  length  of  spans  may  be 
determined;  then  the  general  style  of  bridge,  whether  deck 
or  through,  the  kind  of  trusses  or  girders,  together  with 
panel  lengths  and  depths,  and  the  width  of  bridge,  are 
selected.  In  general,  deck  bridges  should  be  used  when 
possible,  as  they  are  somewhat  more  economical  and,  on 


BRIDGE  SPECIFICATIONS 


r  'T 

0  i 


account  of  the  transverse  bracing  between  the  trusses,  some¬ 
what  stiffer  than  through  bridges;  their  use  is  limited,  how¬ 
ever,  to  locations  where  there  is  plenty  of  room  below  the 
floor.  The  kind  of  structure — plate  girders,  riveted  or  pin- 
connected  trusses,  etc. — depends  on  the  span;  the  style  of 
truss — Pratt,  Warren,  Baltimore,  etc. — is  left  to  the  judgment 
of  the  engineer.  The  depth  and  panel  length  are,  as  a  rule, 
controlled  by  the  specifications;  but  a  few  words  may  be 
added.  It  has  been  found  in  practice  that  for  through  plate- 
girder  bridges,  panel  lengths  of  10  to  15  feet  are  best;  for 
riveted  truss  bridges, 
from  15  to  20  feet;  and 
for  pin-connected  truss 
bridges,  from  20  to 
30  feet.  Panels  may  be 
made  longer  than 
30  feet  in  spans  greater 
than  250  feet  in  length, 
but  for  shorter  spans  it 
is  better  not  to  exceed 
this  limit. 


230.  Width  and 
Clear  Height. — The 
width  and  clear  height 
must  be  sufficient  to  ac¬ 
commodate  the  traffic. 

For  railroad  bridges, 
they  depend  on  the  out¬ 
side  dimensions  of  the  fig.  io 

car  or  engine  having  the  largest  cross-section;  or,  since  one 
car  may  have  the  greatest  width  and  another  the  greatest 
height,  the  outside  dimensions  of  a  car  that  would  have  that 
width  and  height.  This  is  usually  referred  to  as  the  maxi¬ 
mum  equipment.  The  dotted  lines  in  Fig.  10  represent 
the  approximate  outline  of  the  maximum  equipment  in  use 
on  steam  railroads  in  the  United  States,  the  full  lines  form¬ 
ing  the  diagrams  given  in  Figs.  1  and  2.  The  lattpr  are 


58 


BRIDGE  SPECIFICATIONS 


§74 


commonly  spoken  of  as  clearance  diagrams.  Their  lines 
are  located  somewhat  outside  the  lines  of  the  maximum 
equipment  to  give  required  clearance,  so  as  to  keep  unlooked- 
for  projections,  such  as  heads  and  arms  out  of  car  windows, 
from  striking  any  part  of  the  bridge.  The  additional  height 
at  the  top  is  to  prevent  any  part  of  the  overhead  bracing 
from  striking  the  heads  of  brakemen  on  top  of  the  cars. 
Owing  to  difficulties  of  design,  the  top  flanges  of  through 
plate  girders  are  allowed  to  come  closer  to  the  lower  part  of 
the  outline  of  maximum  equipment  than  any  part  of  truss 
bridges.  The  same  clearance  diagram  should  be  used  for 
bridges  on  railroads  that  are  undergoing  electrification,  that 
is,  on  which  the  motive  power  is  being  changed  from  steam 
to  electricity,  as  well  as  on  roads  that  are  built  especially  for 
heavy  cars  operated  by  electricity  on  private  right  of  way 
for  freight  and  passenger  service.  The  indications  at  pres¬ 
ent  are  that  the  equipment  on  such  roads  will  be  as  large 
as  the  largest  now  in  use  on  steam  railroads. 

As  the  equipment  on  street  railroads  is  somewhat  smaller 
than  on  steam  or  heavy  electric  roads,  less  width  and  height, 
need  be  provided.  Fig.  4  represents  the  outline  of  one-half 
the  clearance  diagram  used  on  street  railways.  Less  clear¬ 
ance,  is  needed  above  the  cars  than  on  steam  roads,  as  it  is 
not  necessary  to  allow  for  men  standing  on  top  of  the  cars, 
but  simply  to  provide  ample  room  for  the  trolley. 

On  both  steam  and  electric  roads,  more  clearance  is  allowed 
at  the  sides  on  curves  than  on  straight  track,  as  parts  of  the 
cars  overhang  the  track  and  the  tops  lean  over. 

231.  The  width  of  a  highway  bridge  depends  altogether 
on  the  amount  and  kind  of  traffic  to  be  provided  for.  For 
country  bridges,  the  clear  width  should  never  be  less  than 
about  18  feet;  for  suburban  and  city  bridges,  the  width  may 
be  anything  from  about  20  feet  to  the  full  width  of  the  street 
leading  to  the  bridge.  Each  case  must  be  decided  by  the 
local  requirements. 

232.  Floor  System. — The  arrangement  of  stringers 
and  fiporbeams  depends,  to  a  great  extent,  on  the  allowable 


§74 


BRIDGE  SPECIFICATIONS 


59 


depth  of  floor  from  the  surface  to  the  underneath  clearance 
line.  As  a  rule,  it  is  well  to  have  as  much  depth  as  possible. 
Two-truss  bridges  are  preferred,  as  a  center  truss  requires 
the  spreading  of  the  tracks  or  roadways.  When  two-truss 
bridges  are  used,  the  depth  of  the  floorbeams  and  that  of  the 
floor  are  much  greater  than  for  three-truss  bridges.  In  the 
elimination  of  grade  crossings,  and  frequently  in  other  cases, 
it  is  exceedingly  expensive  to  separate  the  grades  enough  to 
permit  the  use  of  deep  floorbeams;  and  it  is  then  advisable 
at  times  to  spread  the  track  on  railway  bridges,  or  separate 
the  roadways  on  highway  bridges,  so  as  to  allow  for  the 
insertion  of  a  center  truss.  In  such  cases,  the  floorbeams 
need  not  be  so  deep,  as  they  will  be  but  one-half  as  long  as 
if  two  trusses  were  used. 

Some  engineers  think  it  is  best  to  place  the  stringers  of 
railroad  bridges  .directly  under  the  rails,  but  it  seems  better 
practice  to  space  them  6  feet  6  inches  center  to  center,  each 
one  about  9  inches  from  the  center  of  the  rail.  In  this  way, 
some  of  the  shock  and  vibration  of  the  train  is  absorbed  by 
the  elasticity  of  the  ties,  which  have  a  chance  to  deflect. 

Two  stringers  are  frequently  placed  close  side  by  side  to 
carry  the  load  on  each  rail,  but  this  is  not  good  practice,  as 
it  is  almost  impossible  to  distribute  the  load  equally  between 
them  on  account  of  poor  fitting  of  ties,  etc.  If  this  inequality 
occurs  at  the  center  of  a  panel,  the  stringer  getting  the 
greater  part  of  the  load  will  deflect,  thereby  transmitting 
some  of  the  load  to  the  other  stringer,  and  not  much  harm 
will  result.  If  the  inequality  occurs  at  the  end  of  a  panel,  the 
rivets  connecting  one  of  the  stringers  to  the  floorbeam  web 
are  liable  to  get  the  load  that  should  go  through  two  sets  of 
rivets;  they  will  be  overstrained,  and  may,  in  time,  loosen. 
When  stringers  are  riveted  to  floorbeam  webs,  it  is  better  to 
use  one  stringer  for  each  rail. 

233.  Short-span  I-beam  bridges  for  railroads  are  com¬ 
posed  of  two  or  three  beams  for  each  rail.  The  beams  are 
placed  close  together,  and  are  made  to  act  as  one  beam  by 
being  firmly  bolted  together  and  held  in  place  by  separators. 


BRIDGE  SPECIFICATIONS 


74 


GO 


There  is  then  no  objection  to  using  more  than  one  beam 
under  a  rail.  If  the  stringers  in  floor  systems  were  laid 
close  and  bolted  together  in  the  same  way,  it  would  be 
impossible  to  get  satisfactory  connections  to  the  floorbeams. 


234.  Deck  truss  railroad  bridges  are  occasionally  built 
with  a  floor  system,  the  ties  resting  on  the  top  chords  of  the 


o 

o 

o 

o 

o 

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Fig.  11 


trusses.  The  sections  of  top  chord  then  act  as  beams  as  well 
as  compression  members,  and  are  subjected  to  simultaneous 
compressive  and  bending  stresses.  This  practice  is  con¬ 
demned  by  the  best  engineers.  It  is  best  in  all  cases  to 
provide  a  floor  system  in  the  top  chord,  the  ends  of  the  floor- 
beams  being  connected  to  the  insides  of  the  trusses  or  resting 
on  top  of  the  trusses  at  the  panel  points. 


§74 


BRIDGE  SPECIFICATIONS 


61 


235.  Dive  Loads. — One  of  the  most  important  steps  in 
the  design  of  a  bridge  is  to  ascertain  the  live  or  moving  load 
the  bridge  is  to  carry.  The  live  load  on  a  railroad  bridge 
consists  of  locomotives  and  cars.  As  explained  in  Stresses 
in  Bridge  Trusses ,  Part  4,  it  is  customary  to  use  typical  load¬ 
ings  that  represent  the  heaviest  loads  it  is  expected  the 
bridge  will  ever  have  to  carry.  Fig.  11  shows  four  typical 
loadings  in  use  on  leading  railroads  in  the  United  States; 
Cooper’s  loadings  also  have  been  adopted  by  many  of  the 
leading  railroad  companies.  At  the  present  time,  Cooper’s 
E50  well  represents  the  heaviest  loads  on  most  American 
railroads.  In  a  few  special  cases,  where  the  loads  in  use  are 
somewhat  heavier  than  this,  each  load  of  Cooper’s  E50  may 
be  multiplied  by  1.1  or  1.2,  as  desired,  giving  what  may  be 
called  E55  and  E60,  respectively,  approximately  equivalent 
to  the  actual  loads,  and  the  resultant  systems  substituted  for 
E50  in  the  specifications.  For  bridges  on  branch  lines  and 
on  lines  on  which  the  locomotives  and  cars  are  light,  E40 
will  give  sufficiently  heavy  loads.  In  case  extra  heavy  loco¬ 
motives  and  cars  are  used  for  any  purpose,  the  bridges  on 
lines  over  which  they  operate  should  be  designed  for  the 
actual  loads,  increased  10  per  cent,  in  some  cases  to  allow 
for  future  increase. 


236.  Up  to  the  present  time,  the  only  type  of  concen¬ 
trated  load  that  has  been  considered  for  railroad  bridges  has 
been  the  steam  loco¬ 


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*5.0* 

motive  and  train  of 
cars.  There  are  now 
in  use  electric  loco¬ 
motives  very  nearly 
equal  in  weight  to  the  steam  locomotives.  Fig.  12  shows 
the  distances  between  axles  and  the  weights  on  the  axles  of 
one  of  the  heaviest  electric  locomotives  that  has  been  built. 
Bridges  over  which  such  heavy  locomotives  are  to  pass,  or 
over  which  it  is  likely  they  will  pass  in  the  future,  should  be 
designed  for  Cooper’s  E50,  in  the  same  way  as  other  railroad 
bridges,  or  for  the  actual  loads,  as  explained  above. 


62 


BRIDGE  SPECIFICATIONS 


74 


237.  On  electric  roads  designed  for  the  multiple-unit 
system,  which  uses  no  locomotives,  each  car  carrying  its 
own  motors,  it  is  necessary  to  ascertain  if  there  is  any  possi¬ 
bility  of  the  road  being  used  in  the  future  by  steam  or  electric 
locomotives;  if  so,  due  allowance  should  be  made  so  that  the 
bridges  will  be  strong  enough  for  them.  If  it  is  likely  that 
nothing  but  the  cars  will  ever  run  on  the  road,  the  bridges 
should  be  designed  for  the  actual  weights  of  the  cars  when 
fully  loaded,  increased  10  or  20  per  cent,  to  provide  for  a 
possible  increase  in  the  weight  of  future  cars.  Fig.  13  rep- 


1 


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■25  — 


.  Q .  Q _ Q  Q - 

-4-6,A*—/5'-*6,l — 25‘ 


o  o 
o  o 
O  o 
10  10 
<N  CM 


O  O  O  O 

o  o  o  o 

o  o  o  o 

10  10  ,  10  10 

ot  04  j  I  CM  CM 


o  o  o  o 

o  o  o  o 

o  o  o  o 

10  10  ,  in  10 

CM  CM  [ |  CM  CM 


l±. 


Q 


Q-Q  Q-Q. 


:± 

55^ 


Q  ClQ 


45- 


—26 
5.5 


■  VC 


5.5 


26 

(b) 
Fig.  13 


5.5 


K. 


5.5‘ 


-26 


resents  the  weights  and  axle  spacing  of  the  cars  run  by  the 
multiple-unit  system  on  two  different  roads.  The  specifi¬ 
cations  given  for  railroad  bridges  should  be  used  for  such 
system  of  loading,  except  that  the  new  loading  should  be 
substituted  for  that  given  in  Art.  24. 

238.  The  loads  to  which  highway  bridges  are  subjected 
differ  considerably  from  those  to  which  railroad  bridges  are 
subjected.  They  usually  consist  of  heavy  snowfalls,  crowds 
of  people,  wagons,  road  rollers,  and  street  cars.  It  has 
been  observed  that  city  bridges  are  more  likely  to  be  sub¬ 
jected  to  the  weight  of  large  crowds  of  people  and  of  wagons 
than  country  bridges;  a  crowd  of  people  may  cover  the 
entire  floor  of  a  short  span,  but  is  not  likely  to  cover  the 
whole  floor  of  a  long  span.  For  this  reason,  the  uniform 
load  per  square  foot  that  is  used  is  heavier  for  city  than  for 
country  bridges,  and  heavier  for  short  than  for  long  spans. 


74 


BRIDGE  SPECIFICATIONS 


63 


Heavier  road  rollers  are  used  on  city  streets  than  on  country 
roads.  The  case  of  street  cars,  however,  is  somewhat  differ¬ 
ent.  The  heaviest  cars  run  in  city  streets  are,  as  a  rule, 
those  that  are  used  for  interurban  traffic;  that  is,  to  connect 
cities.  These  cars  cross  country  bridges  as  'well  as  city 
bridges,  and  both  kinds  of  bridges  must  be  designed  to  sup¬ 
port  them.  The  loads  given  in  Art.  98  represent,  as  near 
as  possible,  those  to  which  the  different  bridges  may  be  sub¬ 
jected,  and  are  approximately  the  same  as  those  now  in  use 
by  the  best  engineers.  It  is  not  probable  that  they  will 
increase  for  a  great  many  years. 

239.  Impact  and  Vibration. — As  explained  in  Strength 
of  Materials,  Part  1,  a  load  that  is  suddenly  applied  produces 
twice  as  great  a  stress  as  one  that  is  gradually  applied,  and 
a  load  that  is  applied  in  a  very  short  interval  of  time  causes  a 
stress  greater  than  that  caused  by  a  load  that  is  gradually 
applied,  but  less  than  that  caused  by  a  suddenly  applied 
load.  The  moving  loads  that  cross  bridges  are  applied  in  a 
short  interval  of  time,  more  so  in  the  case  of  railroad  than  of 
highway  bridges,  and  it  is  customary  to  make  some  allow¬ 
ance  for  the  resulting  increased  stresses  in  the  members  and 
for  the  shock  and  vibration  of  the  bridge  under  the  passing 
loads.  The  increase  in  the  stresses  is  called  the  effect  of 
impact  and  vibration.  Some  experiments  have  been 
made  and  several  formulas  proposed  for  determining  the 
magnitude  of  this  increase.  Owing,  however,  to  the  difficulty 
and  expense  of  making  experiments,  it  has  been  impossible 
to  obtain  reliable  results.  Practice  varies  considerably  in 
respect  to  the  formula  used;  some  engineers  use  two  values 
for  the  allowable  intensity  of  stress  -  one  for  dead-load  stress, 
and  the  other,  usually  one-half  the  former,  for  live-load 
stress.  This  method  has  the  disadvantage  that  it  causes 
difficulty  in  designing,  especially  in  compression  members; 
it  is  necessary  to  find  separately  the  areas  of  cross-section 
required  to  resist  the  dead-load  and  the  live-load  stresses 
and  to  add  them  in  each  case  to  obtain  the  required  dimen¬ 
sions.  This  method  is,  besides,  illogical,  as  it  tacitly 


BRIDGE  SPECIFICATIONS 


74 


(14 


assumes  that  the  proportional  effect  of  impact  and  vibration 
is  the  same  in  all  members,  while  as  a  matter  of  fact  it  is 
greater  in  such  members  as  floor  members  and  hip  verticals, 
which  receive  their  maximum  live-load  stresses  in  a  short 
interval  of  time  (in  some  cases,  i  second),  than  in  such 
members  as  chords  of  long  spans,  which  do  not  receive  their 
maximum  live-load  stresses  in  so  short  a  time.  The  best 
engineers  allow  the  same  intensity  of  stress  for  both  dead¬ 
load  and  live-load  stresses,  but  add  a  certain  amount  to  the 
live-load  stress  as  calculated  from  the  loading.  In  some 
cases,  the  amount  added  is  a  percentage  of  the  live  load 
equal  to  the  ratio  of  the  live-  to  the  sum  of  the  live-  and  dead¬ 
load  stresses;  but  in  the  great  majority  of  cases  allowance  is 
made  as  specified  in  Arts.  25  and  99.  The  time  required 
for  any  live-load  stress  to  rise  from  zero  to  its  maximum 
depends  on  the  time  it  takes  the  moving  load  to  cover  the 
part  of  the  bridge  that  must  be  loaded  in  order  to  cause  the 
maximum  stress.  The  formulas  just  referred  to  take  this 
into  account;  they  are  the  results  of  experience,  and  are  the 
most  satisfactory  so  far  devised.  More  allowance  is  made  in 
railroad  bridges  than  in  highway  bridges  that  carry  electric 
railways,  as  in  the  former  class  of  bridges  the  loads  move 
much  faster  and  also  cause  more  shock  and  vibration. 


Example  1. — The  live-load  stress  in  the  center  panel  of  the  upper 
chord  of  a  railroad  bridge  truss  150  feet  long  is  280,000  pounds.  What 
amount  must  be  added  for  impact  and  vibration? 

Solution. — In  this  case,  S  =  280,000;  as  the  member  under  con¬ 
sideration  is  a  chord  member,  the  entire  span  must  be  loaded  to 
produce  the  stress  S.  Then  (see  Art."  25),  L  =  150,  and,  therefore, 

/  =  ?9°  x  280,000  =  186,700  lb.  Ans. 

150  -f-  800 

Example  2. — In  a  highway  bridge  truss  125  feet  long,  the  live-load 
stress  in  the  end  post,  due  to  the  load  on  the  car  track,  is  75,000  pounds. 
What  amount  must  be  added  for  impact  and  vibration? 


Solution. — In  this  case,  S  =  75,000;  as  the  member  under  con¬ 
sideration  is  an  end  post,  the  entire  length  of  span  must  be  loaded 
to  produce  the  stress  5\  Then  (see  Art.  99),  L  =  125,  and,  therefore, 


1  = 


300  -  125 


X  75,000  =  13,100  lb. 


Ans. 


1,000 


§74  BRIDGE  SPECIFICATIONS  65 

I 

240.  Reversal  of  Stress. — It  is  a  well-known  fact, 
established  by  experiment,  that  a  piece  of  metal  that  is 
subjected  to  a  large  number  of  repetitions  of  varying 
stresses  will  finally  break,  even  though  the  greatest  stress 
to  which  it  has  been  subjected  is  much  less  than  the  ultimate 
strength  of  the  metal.  This  is  true  whether  the  stresses  are 
of  the  same  kind  or  are  of  opposite  kinds.  Bridge  members 
are  subjected  to  a  great  number  of  repetitions  of  varying 
stresses,  and  various  methods  are  in  use  to  make  allowance 
for  the  effect.  Some  of  these  methods  make  use  of  different 
allowable  intensities  of  stresses  in  different  members,  the 
actual  value  in  any  case  depending  on  the  ratio  of  the  mini¬ 
mum  to  the  maximum  stress.  It  is  the  best  practice  at  the 
present  time,  however,  to  ignore  the  effect  in  those  members 
in  which  the  maximum  and  minimum  stresses  are  of  the 
same  kind,  as  the  range  of  stress  is  comparatively  small, 
and  to  allow  for  it  in  those  members  in  which  the  maximum 
and  minimum  stresses  are  of  opposite  kinds,  as  the  range  of 
stress  is  then  comparatively  large. 

The  customary  way  to  make  allowance  in  those  members 
in  which  the  stress  reverses  is  to  add  to  each  stress  eight- 
tenths  of  the  other  and  then  design  the  member  for  both  of 
the  increased  stresses.  For  example,  if  the  maximum  stress 
in  a  member  is  25,000  pounds  compression,  and  the  minimum 
stress  is  10,000  pounds  tension,  the  member  must  be  designed 
for 

25,000  -f-  A  X  10,000  =  33,000  pounds  compression 
and  for 

10,000  +  A  X  25,000  =  30,000  pounds  tension 

Example. — The  maximum  stress  in  a  member  is  50,000  pounds 
tension,  and  the  minimum  stress  20,000  pounds  compression,  (a)  If 
the  allowable  intensity  of  tensile  stress  is  16,000  pounds  per  square  inch, 

what  is  the  required  net  section  of  the  member?  (6)  If  the  value  of  ^ 

is  such  that  the  allowable  intensity  of  compressive  stress  is  13,500 
pounds  per  square  inch,  what  is  the  required  gross  section? 

Solution.— (a)  The  tension  for  which  the  member  is  to  be  designed 
is  50,000  +  X  20,000  =  66,000  lb. 


135—6 


6  6 


BRIDGE  SPECIFICATIONS 


74 


Then,  the  required  area  of  net  section  is 

66,000  -4-  16,000  =  4.125  sq.  in.  Ans. 

(b)  The  compression  for  which  the  member  is  to  be  designed  is 
20,000  +  -ft  X  50,000  =  60,000  lb. 

Then,  the  required  gross  area  is 

60,000  -T-  13,500  =  4.444  sq.  in.  Ans. 

241.  Dead  Toad. — In  finding  the  dead  load,  it  is  cus¬ 
tomary  first  to  decide  on  the  type  of  floor  and  calculate  its 
weight.  Then  the  approximate  weight  of  the  steelwork  can 
be  calculated  by  some  formula.  The  weight  of  a  bridge  per 
linear  foot  depends  on  the  moving  load  for  which  the 
bridge  is  designed  and  on  the  intensities  of  stress  adopted. 
Formulas  for  calculating  weights  of  bridges  are  purely 
empirical;  they  are  based  on  values  that  have  been  observed 
in  actual  structures.  On  account  of  the  fact  that  railroad 
bridges  are,  as  a  rule,  designed  for  one  loading,  the  formulas 
for  their  weights  are  fairly  reliable.  In  the  case  of  highway 
bridges,  in  which  the  loadings  and  widths  vary  within  a  wide 
range,  it  is  almost  impossible  to  give  formulas  that  represent 
all  the  conditions.  In  any  event,  it  is  necessary,  after  having 
completed  the  design  of  a  bridge,  to  compute  its  weight 
accurately;  if  the  computed  weight  differs  much  from  the 
assumed  weight,  the  dead-load  stresses  should  be  recomputed 
and  the  cross-sections  of  the  members  altered  to  correspond 
with  the  corrected  stresses.  This  is  sometimes  spoken  of.  as 
revising  tlie  design. 


242.  Weights  of  Railroad  Bridges. — The  following 
formulas  give  the  weights  w)  in  pounds  per  linear^  foot,  of 
the  steel  work  in  railroad  bridges  designed  according  to  the 
specifications  from  Arts.  14  to  90  for  Cooper’s  E50,  l  being 
the  span,  in  feet: 

Rolled  I  beams,  zv  —  25  l  for  each  track. 

Deck  plate-girder  bridges,  w  =  500  -f-  8  /  for  one  track. 

Half-through  plate-girder  bridges,  w  =  800  +  12  /  for  one 
track. 

Riveted  truss  bridges, 


w  =  1,500 


for  one  track 


BRIDGE  SPECIFICATIONS 


67 


Riveted  truss  bridges, 


w  —  2,600 


//  -  90\ •" 

V  100  ) . 


for  two  tracks 


Pin-connected  truss  bridges  may  be  assumed  5  per  cent, 
lighter  than  riveted  truss  bridges  for  spans  over  200  feet  in 
length.  For  spans  shorter  than  200  feet,  the  same  formulas 
may  be  used  as  for  riveted  truss  bridges. 

The  above  weights  are  for  bridges  having  standard-tie 
floors,  as  described  in  Art.  48.  Solid-floor  bridges  will,  in 
general,  be  about  25  per  cent,  heavier. 


243.  Weights  of  Highway  Bridges. — The  following 
formulas  give  the  weights  w,  in  pounds  per  linear  foot,  of 
one  girder  or  truss  in  highway  bridges  designed  according  to 
the  specifications  given  in  Arts.  91  to  159;  l  being  the  span, 
in  feet,  and  W  the  maximum  load  per  linear  foot  supported 
by  the  girder  or  truss,  including  the  live  load  together  with 
the  impact,  and  the  weight  of  floorbeams,  stringers,  railings, 
and  floor. 


Plate-girder  bridges,  w 


IV 


Riveted  truss  bridges,  w  — 


1,000 

W 


(24+  .8/). 


12 


1  +  2 


7  -  90V1 

v  100  7  J  • 


Pin-connected  truss  bridges  may  be  assumed  5  per  cent, 
lighter  than  riveted  truss  bridges  for  spans  over  200  feet  in 
length.  For  spans  shorter  than  200  feet,  the  same  formulas" 
may  be  used  as  for  riveted  truss  bridges. 


/ 


DESIGN  OF  PLATE  GIRDERS 

(PART  1*) 


GENERAL  PRINCIPLES 


BEAMS 

1.  Introduction. — The  principles  governing  the  distri¬ 
bution  of  stress  in  the  cross-section  of  a  beam,  and  the  for¬ 
mulas  by  which  the  stresses  are  obtained  from  the  moments  and 
shears,  have  been  explained  in  connection  with  the  theory  of 
beams  in  Strength  of  Materials.  The  formula  for  the  maximum 
tensile  and  compressive  stresses  at  any  section  of  a  beam  is 


Me 


in  which  s  =  maximum  intensity  of  stress; 

c  =  distance  of  most  remote  part  of  section  from 
neutral  axis; 

/  =  moment  of  inertia  of  entire  cross-section  about 
neutral  axis; 

M  =  bending  moment  at  section  considered. 

If  the  expression  -,  which  is  the  section  modulus,  is  repre- 

c 

sented  by  Q ,  the  formula  for  the  maximum  intensity  of  stress 
becomes 

5  =  K 


*A11  the  tables  referred  to  in  this  Section  are  given  in  Bridge  Tables 
and  explained  in  Bridge  Members  and  Details ,  Parts  1  and  2.  In  refer¬ 
ring  to  the  Section  entitled  Bridge  Specifications ,  the  title  will  for 
convenience  be  abbreviated  to  B.  S. 


Copyrighted,  by  International  Textbook  Company.  Entered  at  Stationers'  Hall,  London 

S  75 


9 


DESIGN  OF  PLATE  GIRDERS 


§75 


From  this  formula  follows 


5 


Care  must  be  taken  that  the  proper  units  are  used  in  these 
formulas.  It  is  customary  to  express  5  in  pounds  per  square 
inch,  c  in  inches,  and  M  in  inch-pounds;  the  moment  of 
inertia  /  and  section  modulus  Q  found  from  the  dimensions 
of  the  section  expressed  in  inches. 

2.  I  Beams. — The  maximum  intensity  of  stress  in  an 

M 

I  beam  is  found  by  the  formula  s  =  — .  The  section  moduli 

Q 

of  I  beams  of  different  weights  and  depths  are  given  in 
Table  XIV.  The  practical  problem,  however,  usually  con¬ 
sists  in  finding  what  size  of  I  beam  will  safely  carry  a 
given  load. 

To  solve  this  problem,  the  maximum  bending  moment  M 

M 

is  computed,  and  then,  by  means  of  the  formula  O  =  — ,  the 

required  value  of  the  section  modulus  is  found.  An  I  beam 
having  a  section  modulus  equal  to  or  slightly  greater  than 
that  required  is  then  chosen  from  Table  XIV.  The  same 
method  is  followed  in  designing  channels  to  be  used  as 
beams. 

Example  1. — The  bending  moment  at  a  given  section  of  a  12-inch 
40-pound  I  beam  is  672,000  inch-pounds.  What  is  the  maximum  inten¬ 
sity  of  stress  at  that  section? 

Solution. — Consulting  Table  XIV,  the  section  modulus  of  a  12-in. 
40-lb.  I  beam  is  found  to  be  44.8.  Then,  since  M  is  672,000  in. -lb., 
the  maximum  intensity  of  stress  s  is 

672,000  4-  44.8  =  15,000  lb.  per  sq.  in.  Ans. 

Example  2. — The  maximum  bending  moment  on  a  beam  is 
1,840,000  inch-pounds.  If  it  is  required  that  the  maximum  intensity 
of  stress  shall  not  exceed  16,000  pounds  per  square  inch,  what  size  and 
weight  of  I  beam  must  be  used? 

Solution. — Since  M  is  1,840,000  in. -lb.,  and  s  is  16,000  lb.  per 
sq.  in.,  the  required  value  of  section  modulus  Q  is  1,840,000  4-  16,000 
=  115.  Consulting  Table  XIV,  and  following  from  the  smaller  beams 
toward  the  larger,  the  first  I  beam  that  has  a  section  modulus  as  large 
as  required  is  found  to  be  a  15-in.  95-lb.  beam,  which  has  a  section 


§75 


DESIGN  OF  PLATE  GIRDERS 


3 


modulus  of  116.4.  Looking  lower  down,  however,  it  is  found  that  a 
20-in.  65-lb.  beam  has  a  section  modulus  of  117,  which  is  also  suffi¬ 
cient.  The  latter  beam  should  be  used,  as  it  is  30  lb.  per  ft.  lighter, 
and  therefore  more  economical  than  the  95-lb.  beam. 

Note.— The  advantage  of  using  a  deep  beam  is  here  apparent,  as  the  required 
value  of  section  modulus  can  be  had  with  a  lighter  beam  than  if  a  shallower  beam 
were  used. 


EXAMPLES  FOR  PRACTICE 

1.  The  bending  moment  at  a  given  section  of  a  24-inch  100-pound 

I 'beam  is  3,472,000  inch-pounds.  What  is  the  maximum  intensity  of 
stress  at  that  section?  <  Ans.  17,500  lb.  per  sq.  in. 

2.  The  bending  moment  at  a  given  section  of  an  18-inch  65-pound 

I  beam  is  1,370,600  inch-pounds.  What  is  the  maximum  intensity  of 
stress  at  that  section?  Ans.  14,000  lb.  per  sq.  in. 

3.  The  maximum  bending  moment  on  an  I  beam  is  133,300  foot¬ 
pounds.  What  size  I  beam  must  be  used  in  order  that  the  maximum 
intensity  of  stress  shall  not  exceed  16,000  pounds  per  square  inch? 

Ans.  A  20-in.  65-lb.  I  beam 

4.  The  maximum  bending  moment  on  an  I  beam  is  400,000  inch- 
pounds.  What  size  I  beam  must  be  used  in  order  that  the  maximum 
intensity  of  stress  shall  not  exceed  16,000  pounds  per  square  inch? 

Ans.  A  10-in.  30-lb.  I  beam 


PLATE  GIRDERS 


SECTION  MODULUS 

3.  The  maximum  stresses  due  to  bending  moment  in  a 

M 

plate  girder  may  be  found  by  means  of  the  formula  s  = 

As  the  flanges  are  not  the  same  size  throughout  the  whole 
length  of  the  girder,  however,  the  value  of  Q  changes 
wherever  the  section  of  flange  changes,  and  in  order  to  use 
the  formula  it  is  necessary  to  compute  the  value  of  Q  at 
every  section  where  the  flange  changes.  This  requires 
much  time  and  is  rarely  done  in  practice;  a  modification  of 
the  foregoing  formula  is  used  that  gives  sufficiently  close 
results  and  is  much  more  convenient.  This  formula  will 
now  be  explained. 


4 


DESIGN  OF  PLATE  GIRDERS 


§75 


4.  Let  Fig.  1  be  a  vertical  section  of  a  plate  girder  having 
dimensions  as  follows:  thickness  of  web,  /;  width  (depth)  of 
web,  h\  vertical  distance  between  centers  of  gravity  of  flanges, 
he\  total  height  or  depth  of  section,  kl;  gross  area  of  cross- 
section  of  top  flange  and  net  area  of  cross-section  of  bottom 
flange,  which  will  be  assumed  equal,  A.  It  will  be  assumed 
that  the  cross-section  of  the  girder  is  symmetrical;  then,  the 

neutral  axis  will  be  at  the  center, 
h 

at  a  distance  from  the  center 

of  gravity  of  each  flange.  As 

Q  =  — ,  it  is  necessary  to  compute 
c 

h 

the  value  of  /;  c  is  equal  to  — k 

A 

The  moment  of  inertia  of  the 
entire  cross-section  about  the 
neutral  axis  is  the  sum  of 
the  moment  of  inertia  of  the 
web  about  the  neutral  axis,  the 
moment  of  inertia  of  each  flange 
about  an  axis  parallel  to  the 
neutral  axis  and  passing  through 
the  center  of  gravity  of  the  flange,  and  the  product  of  the 
area  of  each  flange  and  the  square  of  the  distance  from  its 
center  of  gravity  to  the  neutral  axis. 

The  moment  of  inertia  of  the  web  about  the  neutral  axis 
t  h 3 

As  part  of  the  web  is  cut  out  by  rivet  holes,  it  is 


Fig.  1 


IS 


12* 


customary  to  allow  for  the  decrease  in  strength  by  using  for 
the  moment  of  inertia  three-fourths  of  the  theoretical  value; 

t  h3  t  h 3 


that  is,  in  this  case,  i  X 


The  moment  of  inertia 


12  16 

of  each  flange  about  an  axis  through  its  center  of  gravity  is 
very  small  compared  with  the  other  terms,  and  in  practice 
it  is  customary  to  neglect  it.  The  product  of  the  area  of 
each  flange  and  the  square  of  the  distance  of  the  center  of 


gravity  of  the  flange  from  the  neutral  axis  is  A  X 


h. 


For 


§75 


DESIGN  OF  PLATE  GIRDERS 


5 


Therefore,  for  the  moment  of  inertia  of  the  entire  cross- 
section  of  the  girder  about  the  neutral  axis,  we  have, 
approximately, 


whence,  since  Q  —  -,  and  c  =  4-1, 

c  2 


Ah/  ,  th3 

— ---  +  — - 


Ah/.  t h * 


h\  8  h 


2 


This  formula  is  not  convenient  in  this  form.  By  assuming 
that  in  the  first  term  hx  can  be  replaced  by  hg,  and  that  in 
the  second  term  hx  can  be  replaced  by  /z,  and  /z3  by  h 2  X  hg, 
the  following  more  convenient,  and  sufficiently  approximate, 
formula  is  found: 


As  a  matter  of  fact,  k,  hlt  and  hg  are  as  a  rule  very  nearly 
equal,  and  there  is  not  very  much  error  in  assuming  that  any 
of  these  quantities  can  be  replaced  by  either  of  the  other  two. 

Example. — The  web  of  a  plate  girder  is  48  in.  X  i  in.  in  cross- 
section.  Each  flange  has  an  area  of  section  equal  to  20  square  inches, 
and  the  vertical  distance  between  their  centers  of  gravity  is  47  inches. 
What  is  the  section  modulus  of  the  cross-section? 

Solution. — In  this  case,  hg  —  47  in.,  A  =  20  sq.  in.,  t  —  \  in., 
and  h  —  48  in.  Substituting  these  values  in  the  formula, 


Ans. 


DESIGN  OF  FLANGES 


M 


5.  Determination  of  Flange  Area. — Since  s  = 


we  have  also,  M  =  s  Q.  Substituting  for  Q  its  value  given 
in  Art.  4,  this  equation  becomes 


t  h 


6 


DESIGN  OF  PLATE  GIRDERS 


§75 


whence 

M  -  A  1  th 
s  hs  8 

and 

a  _  M  th 

00 

The  expression  ——  is  sometimes  spoken  of  as  the  flange 

she 

area,  and  the  term  —  is  spoken  of  as  the  portion  of  web 

8 

that  goes  to  make  up  the  flange  area,  or  that  assists  in 
resisting  the  bending  moment. 

In  designing,  the  distance  between  the  centers  of  gravity 
of  the  flanges  is  usually  first  assumed  equal  to  the  width  of 
web,  and  the  flange  is  designed  on  that  basis;  then,  the  cor¬ 
rect  distance  is  calculated,  and,  if  necessary,  the  areas  of  the 
flanges  are  changed  to  correspond  with  it. 

6.  Effect  of  Web. — It  is  sometimes  specified  that  the 
flanges  shall  be  considered  as  resisting  the  entire  bending 
moment,  without  considering  the  assistance  of  the  web.  In 
this  case,  as  the  last  expression  in  the  formula  tor  A  in  Art.  5 
represents  the  effect  of  the  web,  it  is  simply  necessary  to 
omit  it.  The  resulting  formula  is 

A=™ 

s  hg 

By  using  this  formula,  the  area  of  each  flange  is  made 
larger  than  necessary  by  an  amount  equal  to  one-eighth  the 
cross-section  of  the  web.  This  assumption  evidently  gives 
incorrect  results;  but,  as  it  provides  more  flange  area  than  is 
required,  it  is  on  the  safe  side.  The  only  objection  to  it  is 
that  it  is  not  economical.  In  the  following  articles,  it  will  be 
assumed  that  the  web  assists  in  resisting  bending  moment. 

Example. — A  plate  girder  having  a  60"  X  web  is  subjected  to  a 
maximum  bending  moment  of  2,000,000  foot-pounds.  If  the  allowable 
intensity  of  bending  stress  is  16,000  pounds  per  square  inch,  what  is 
the  trial  value  that  would  be  used  for  the  area  of  each  flange:  (a)  if 
the  web  is  assumed  to  assist  in  resisting  the  bending  moment?  (£)  if  the 
flanges  are  assumed  to  resist  the  entire  bending  moment? 

Solution. — (a)  As  the  bending  moment  is  given  in  foot-pounds, 
it  must  be  multiplied  by  12,  in  order  to  reduce  it  to  inch-pounds. 
This  gives  M  =  12  X  2,000,000  =  24,000,000  in. -lb.  The  value  of  s 


§75 


DESIGN  OF  PLATE  GIRDERS 


7 


is  16,000  lb.  per  sq.  in.  As  the  trial  values  of  the  areas  are  required, 
the  trial  value  of  hg,  that  is,  the  width  of  the  web,  or  60  in.,  will  be 
used.  In  the  first  case,  the  required  area  of  the  flange  is  given  by 
the  formula  in  Art.  5, 

_  M_  _  t  h 
A  ~  shg  8 

Here,  t  =  J-  in.,  and  h  =  hz  =  60  in.  Then,  substituting  in  the 
formula, 


A  = 


24,000,000  .375  X  60 


25  —  2.81  =  22.19  sq.  in.  Ans. 


16,000  X  60  8 

( b )  In  the  second  case,  the  required  area  of  flange  is  given  by  the 
M 

formula  A  =  j^-.  Substituting  the  given  values, 

*  24,000,000 

A  "  16,000  X  60  “  25  Sq'  m'  AnS' 


7.  Length  of  Flange  Members.- — As  the  bending 
moment  near  the  end  of  a  girder  is  less  than  at  the  center, 
the  required  area  of  flange  section  is  less  near  the  end  than 
at  the  center.  For  this  reason,  each  flange  is  composed  of 
several  parts,  usually  two  angles  and  one  or  more  plates. 
The  angles,  and  in  some  cases  one  plate,  are  continued  the 
entire  length  of  the  girder;  the  other  plates  are  shorter,  and 
are  cut  of!  where  they  are  no  longer  required.  It  is  very 
difficult  to  find,  by  the  analytic  method,  the  sections  at  which 
the  different  flange  plates  are  no  longer  required;  a  combina¬ 
tion  of  the  analytic  and  the  graphic  method  is  more  con¬ 
venient.  The  required  areas  of  flange  at  several  sections 
along  the  girder  are  computed  by  means  of  the  formula 

M 

A  =  - ,  and  a  curve  of  flange  areas  is  drawn.  Fig.  2 

s  hs 

shows  the  curves  for  the  top  and  bottom  flanges  of  a  plate 
girder,  and  the  graphic  method  of  determining  the  sections  at 
which  the  plates  are  no  longer  required.  As  plate  girders  are 
usually  symmetrical  about  the  center,  only  one-half  of  the  span 

is  shown.  The  diagram  is  explained  in  the  following  article. 

/ 

8.  Curve  of  Flange  Areas. — On  any  line  X'  X,  Fig.  2, 
the  distance  jR  O  is  laid  off  to  scale  equal  to  one-half  the  span, 
and  the  sections  A,  B ,  C,  etc.,  at  which  the  flange  areas  have 
been  computed,  are  marked  in  their  proper  positions.  At 
A ,  A,  C,  etc.,  lines  are  drawn  at  right  angles  to  X'  X,  and  on 


8  DESIGN  OF  PLATE  GIRDERS  §75 

♦ 

them  are  laid  off  to  scale  the  distances  A  A',  B  B' ,  CO,  etc., 
above  and  below  X'Xto  represent  the  values  of  A  as  found  by 

M 

the  formula^  = - .  If  the  load  on  the  girder  is  concentrated 

she 

at  the  points  A,  B,  C,  etc.,  as  in  a  half-through  plate-girder 
bridge,  straight  lines  R  A',  A'  B',  B'  C',  etc.  are  drawn  con¬ 
necting  the  points  just  found;  if  the  load  on  the  girder  is 


distributed,  as  in  a  deck  plate-girder  bridge,  smooth  curves 
are  passed  through  the  points  R,  A',  B’ ,  O ,  D',  and  I',  above 
and  below  the  line  X'  X,  respectively.  In  the  present  case, 
it  has  been  assumed  that  the  load  is  uniformly  distributed; 
then,  the  curves  R  If  are  the  curves  of  flange  areas,  and  the 
ordinate  at  any  section,  such  as  EE '  at  E ,  represents  the 
required  flange  area  at  that  section.  The  next  step  in 
the  construction  of  the  diagram  consists  in  laying  off  to 
scale  on  the  line  Y O  Y'  at  right  angles  to  X'  X  at  O  the 
areas  of  the  different  sections  that  make  up  the  flanges. 
When  it  is  specified  that  the  effect  of  the  web  in  assisting  to 
resist  the  bending  moment  is  to  be  neglected,  the  areas  of 


§75 


DESIGN  OF  PLATE  GIRDERS 


9 


the  angles  and  plates  are  laid  off  directly  from  O;  when  it  is 
specified  that  the  effect  of  the  web  is  to  be  considered,  as  in 
the  present  case,  the  points  O'  are  located  on  Y  O  Yf  at  such 


t  h 

a  distance  from  O  that  O  O'  represents  to  scale  — ,  and  the 


lines  O' R'  are  drawn  parallel  to  OR.  Then,  the  ordinates 
between  the  lines  O' R'  and  the  curves,  at  any  section,  such 
as  E"  E'  at  E ,  represent  the  required  area  that  must  be  pro¬ 
vided  in  the  angles  and  plates  at  that  section.  In  the  present 
case,  it  will  be  assumed  that  two  angles  and  three  plates  are 
required  at  the  center  in  each  flange;  O' E  represents  the 
gross  area  of  the  two  angles,  and  EG,  G  H,  and  HI,  the  gross 
areas  of  the  three  plates  in  the  top  flange;  OfFl,  E1  G„  GXHX, 
and  Hx  7T  represent  the  net  areas  of  the  angles  and  plates 
in  the  bottom  flange.  Lines  are  drawn  through  the 
points  F,  G ,  H ,  etc.  to  their  intersections  F' ,  G' ,  H',  etc., 
respectively,  with  the  curve;  then,  f,g,  etc.,  on  perpendiculars 
from  F1,  G',  etc.  to  X'  X,  are  the  sections  at  which  the  dif- 
erent  flange  plates  are  no  longer  required. 

For  example,  it  is  seen  that  at  the  section  h  the  required 
area  of  the  top  flange  is  represented  by  h' H' ,  which  is  equal 
to  O' H,  and  this  represents  the  sum  of  the  areas  of  the  two 
angles  and  two  plates.  Hence,  as  the  outside  plate  is  not 
required,  it  can  be  discontinued  at  H',  and  H H'  will  repre¬ 
sent  one-half  its  length.  In  a  similar  manner,  at  the  section  ^ 
the  required  area  of  the  top  flange  is  represented  by  g'Gf, 
which  is  equal  to  O' G,  and  this  represents  the  sum  of  the 
areas  of  the  two  angles  and  one  plate.  Hence,  as  the  two 
outside  plates  are  not  required,  the  second  plate  can  be 
discontinued  at  G'.  By  the  same  method,  the  section  at 
which  any  plate  is  no  longer  required  can  be  found  when 
there  are  any  number  of  plates. 


EXAMPLES  FOR  PRACTICE 

1.  The  web  of  a  plate  girder  is  84  in.  X  Te  in-  m  cross-section. 
Each  flange  has  an  area  of  section  equal  to  36  square  inches,  and  the 
vertical  distance  between  their  centers  of  gravity  is  83  inches.  What  is 
the  section  modulus  of  the  cross-section?  Ans.  3,478 


10 


DESIGN  OF  PLATE  GIRDERS 


§75 


2.  A  plate  girder  having  a  56"  X  web  is  subjected  to  a  maximum 
bending  moment  of  1,792,000  foot-pounds.  If  the  allowable  intensity 
of  bending  stress  is  16,000  pounds  per  square  inch,  what  is  the  trial 
value  that  would  be  used  for  the  area  of  cross-section  in  the  design  of 
each  flange:  ( a )  if  the  web  is  assumed  to  assist  in  resisting  the  bend¬ 
ing  moment?  (£)  if  the  flanges  are  assumed  to  resist  the  entire 

bending  moment?  .  f  (a)  20.5  sq.  in. 

Ans‘  \  (b)  24  sq.  in. 

3.  The  required  flange  areas  at  several  sections  of  a  deck  plate 
girder  64  feet  long  are  as  follows:  at  8  feet  from  the  end,  21  square 
inches;  at  16  feet  from  the  end,  36  square  inches;  at  24  feet  from  the 
end,  45  square  inches;  and  at  the  center  of  the  span,  48  square  inches. 
The  upper  flange  is  made  up  as  follows: 


Square  Inches 

th  +  8 . =  4.1  2 

Two  angles,  6  in.  X  6  in.  X  f  in.  @  8.44 . =1  6.8  8 

Three  plates,  16  in.  X  tit  in.  @  7.00 . =2  1.0  0 

One  plate,  16  in.  X  f  in.  @  6.00 . =  6.0  0 

I~84M) 


What  are  the  theoretical  lengths  of  the  four  flange  plates  to  the 
next  larger  whole  foot?  Ans.  23  ft.;  34  ft.;  42  ft.;  48  ft. 


DESIGN  OF  WEB 

9.  Longitudinal  Shearing  Stress. — The  distribution 
of  stress  in  the  cross-section  of  a  beam  can  be  represented 
as  in  Fig.  3,  in  which  the  lines  with  arrowheads  represent 

the  intensities  of  stress  at  different 
distances  from  the  neutral  axis.  All 
the  stresses  acting  on  the  section 
above  the  neutral  axis  are  in  one 
direction;  all  below,  in  the  other 
direction.  On  this  account,  there  is 
a  tendency  for  the  portion  of  the 
beam  on  one  side  of  the  neutral 
plane  to  slide  horizontally  on  the 
portion  on  the  other  side.  The 
same  is  true  at  any  horizontal  sec¬ 
tion,  such  as  xx ,  the  part  above  xx 
tending  to  slide  on  or  shear  away  from  the  part  below  the 
plane  x  x.  This  tendency  causes  a  shearing  stress  called  the 
longitudinal  shearing  stress  or  longitudinal  shear, 


Fig.  3 


§75  '  DESIGN  OF  PLATE  GIRDERS 


11 


which  decreases  as  the  distance  from  the  neutral  axis 
increases,  is  greatest  at  the  neutral  axis,  and  is  zero  at  the 
outside  of  the  section.  It  can  be  shown  by  advanced  mathe¬ 
matics  that  the  longitudinal  shearing  stress  in  a  beam  is  given 
by  the  formula 

//  /_ 

(1) 


Sx'  = 


VG 


I 


in  which  s/  =  longitudinal  stress,  in  pounds  per  linear  inch 

of  beam  (that  is,  the  stress  that  would 
occur  in  a  length  of  the  beam  equal  to 
1  inch,  if  the  stress  in  all  that  portion  had 
the  same  intensity  as  at  the  section  con¬ 
sidered); 

V  =  maximum  vertical  shear,  in  pounds,  on  the 
section  considered; 

/  =  moment  of  inertia,  about  the  neutral  axis,  of 
the  entire  section,  derived  from  the  dimen¬ 
sions  of  the  cross-section  in  inches; 

G  =  static  moment,  about  neutral  axis,  of  all  that 
part  of  section  outside  of  point  considered 
(that  is,  the  product  of  the  area  of  that 
part  of  the  section  and  the  distance  from 
its  center  of  gravity  to  the  neutral  axis). 

If  the  thickness  of  the  beam  is  denoted  by  /,  the  inten¬ 
sity  Sx  of  longitudinal  shear,  per  square  inch,  is  equal  to 
sS  -r-  t\  that  is, 


(2) 


In  calculating  longitudinal  shear,  it  is  immaterial  whether 
the  vertical  shear  is  positive  or  negative,  as  only  the  numer¬ 
ical  value  is  required. 


10.  Variation  in  Shearing  Stress. — As  the  vertical 
shear  V is  greater  near  the  end  than  at  the  center,  the  longi¬ 
tudinal  shear  is  also  greater  at  the  end  than  at  the  center. 
Considering  a  vertical  section  of  the  beam,  V  and  /  are  con¬ 
stant  for  that  section;  that  is,  they  do  not  vary,  no  matter 
what  part  of  the  section  is  considered;  G  decreases  as  the 
point  at  which  the  longitudinal  shear  is  desired  is  taken 


12 


DESIGN  OF  PLATE  GIRDERS 


75 


farther  from  the  neutral  axis,  and  is  zero  at  the  outside  of 
the  section.  Therefore,  according-  to  formula  2,  Art.  9,  the 
maximum  intensity  of  longitudinal  shear  occurs  &t  the  neutral 
axisy  near  the  end  of  the  span. 


11.  Web  Shear. — It  can  be  shown  that  the  intensity  of 
vertical  shearing  stress  at  any  point  in  the  cross-section  of  a 
beam  is  equal  to  the  intensity  of  longitudinal  shear  at  the 
same  point.  The  maximum  intensity  of  vertical  shear  at  any 
section  of  a  plate  girder  can  therefore  be  found  by  applying 


the  formula  Sy  = 


VG 

tl 


to  a  point  at  the  neutral  axis  of  the  sec¬ 


tion.  In  Art.  4,  it  was  found  that  the  value  of  /  is  approxi- 

The  static  moment  G  is  the  sum  of 


.  .  A  hg  .  t  Id 
tnately  -g-  +  — 


the  static  moment  of  the  area  A  of  one  flange  and  the 

t  h 


static  moment  of  the  area 


2 


The  distance  of  the  center 


h £ 


of  gravity  of  A  from  the  neutral  axis  is  and,  therefore, 

2 

h 

the  static  moment  of  A  is  A  X  -P.  The  distance  of  the  center 

A 

of  gravity  of  the  area  of  one-half  the  web  from  the  neutral 

axis  is  and,  therefore,  the  static  moment  of  that  area  is 
4 

th  h  _  th 2 

y  x  i  ~  ir 


Therefore, 


r  —  A  .  t  h* 

~2~  +  IT 


Substituting  in  formula  2,  Art.  9,  the  values  just  found 
for  /  and  G ,  there  results 


= 


7 y  ( hg  .  t  h 
\  2  8 
,lAh;  ,  th3 
'  \  2~  +  16 


(1) 


t  h *  t  h3 

As  the  terms  — -  and  — r  are  small,  compared  to  the  other 

8  16 

terms,  they  may  be  omitted  without  any  error  worth  consid¬ 
ering  in  practice.  Formula  1  then  becomes 


75 


DESIGN  OF  PLATE  GIRDERS 


13 


VX 


A  he, 


s  i  = 


t  x  AX- 


V 

t  her 


or,  approximately,  since  hs  is  very  nearly  equal  to  hy 

■•-ii  <» 


The  product  th  is  equal  to  the  area  of  cross-section  of  the 
web.  Formula  2  may,  therefore,  be  stated  in  the  form  of  a 
rule  as  follows: 


Rule. — To  find  the  maximum  intensity  of  shearing  stress  in 
the  web  of  a  plate  girder  at  any  section ,  divide  the  maximum 
vertical  shear,  in  pounds ,  by  the  gross  area  of  cross-section  of  the 
web  in  square  inches . 


12.  Stiffeners. — In  Bridge  Members  and  Details ,  it  was 
explained  that  a  flat  plate,  such  as  the  web  of  a  plate 
girder,  tends  to  buckle  when  subjected  to  a  shearing  stress, 
and  for  this  reason  it  is  stiffened  by  angles  riveted  to  the 
sides  of  the  plate.  The  holes  for  the  rivets  in  the  stiffeners 
decrease  the  cross-section  of  the  plate,  and  it  has  been  found 
in  practice  that  the  effective  or  net  section  through  such  a 
row  of  holes  is  very  nearly  75  per  cent,  of  the  gross  section. 
To  allow  for  the  decrease  in  section,  it  is  customary  to 
specify  that  the  intensity  of  shearing  stress  found  by  the 

formula  sx  —  at  any  point  shall  not  exceed  75  per  cent. 
t  h 

of  the  allowable  intensity  of  shearing  stress. 


Example  1. — The  maximum  vertical  shear  at  a  given  section  of  a 
plate  girder  is  180,000  pounds,  and  the  area  of  cross-section  of  the  web 
is  30  square  inches.  What  is  the  maximum  intensity  of  shearing  stress? 

Solution. — In  this  case,  V  is  180,000  lb.  and  th  is  30  sq.  in.  Sub¬ 
stituting  in  formula  2,  Art.  11, 

sx  =  180,000  -7-  30  =  6,000  lb.  per  sq.  in.  Ans. 

Example  2. — The  maximum  vertical  shear  at  a  given  section  of  a 
girder  is  240,000  pounds.  If  the  width  of  web  is  72  inches,  and  the 
clear  unsupported  distance  at  the  given  section  is  26  inches,  what 
thickness  must  be  used  in  order  that  the  intensity  of  shearing  stress 
shall  not  exceed  the  values  given  in  Table  XXXVI? 


135—7 


14 


DESIGN  OF  PLATE  GIRDERS 


75 


Solution.— In  an  example  of  this  kind,  which  is  common,  it  is 
necessary  to  assume  either  the  intensity  of  shearing  stress  or  the  thick¬ 
ness  of  web.  The  experienced  designer  can,  as  a  rule,  assume  the 
thickness  of  web  pretty  close  to  the  actual  thickness,  and  later  correct 
his  assumption.  In  the  present  case,  the  intensity  cannot  exceed 
9,000  lb.  per  sq.  in.  (see  Table  XXXVI);  therefore,  the  cross-section  of 
the  web  cannot  be  less  than  240,000  4-  9,000  =  26.667  sq.  in.,  and  the 
thickness  cannot  be  less  than  this  divided  by  the  height,  or  26.667  4-  72 
=  .37  in. ,  say  in.  The  area  of  cross-section  of  a  72"  X  I"  plate  is 
27  sq.  in.;  then,  the  actual  intensity  of  shear,  if  a  J-in.  plate  is  used, 
will  be  240,000-7-27  =  8,888  lb.  per  sq.  in.  Consulting  Table  XXXVI, 
it  is  found  that  the  allowable  intensity  of  shear  in  a  -f-in.  plate  with 
an  unsupported  width  of  26  in.  is  4,600  lb.  per  sq.  ip.  As  this  is  so 
much  less  than  the  actual  intensity,  a  thicker  plate  must  be  tried.  The 
difference  between  the  actual  and  the  allowable  intensity  being  so 
great,  the  next  thickness,  fa  in.,  will  not  be  considered,  but  a  plate 
■£-in.  thick  will  be  tried. 

The  area  of  cross-section  of  a  72"  X  plate  is  36  sq.  in.;  then,  the 
actual  intensity  of  shear,  if  a  ^-in.  plate  is  used,  will  be  240,000  4-  36 
=  6,667  lb.  per  sq.  in.  Consulting  Table  XXXVI,  it  is  found  that  the 
allowable  intensity  of  shear  is  6,400  lb.  per  sq.  in.  As  this  is  less  than 
the  actual  intensity,  a  thicker  plate  must  be  used.  The  next  thickness, 
that  is,  -pg-  in.,  will  be  tried.  The  area  of  cross-section  of  a 
72"  XiV;  plate  is  40.5  sq.  in.;  then,  the  actual  intensity  of  shear,  if  a 
-j^g-in.  plate  is  used,  will  be  240,000  4-  40.5  =  5,930  lb.  per  sq.  in. 

Consulting  Table  XXXVI,  it  is  found  that  the 
allowable  intensity  of  shear  is  7,000  lb.  persq.  in.  As 
this  is  greater  than  the  actual  intensity,  the  assumed 
thickness  is  sufficient.  Therefore,  a  72"  X  fa"  plate 
may  be  used. 

13.  Pitch  of  Flange  Rivets. — The 
longitudinal  shear  in  a  beam  of  solid  cross- 
section  is  resisted  by  the  shearing  strength 
of  the  material.  That  in  a  beam  built  up  of 
various  simple  rolled  sections  is  resisted  by 
the  rivets  that  hold  the  different  parts  together 
so  as  to  make  them  act  as  one  piece.  The 
longitudinal  shearing  stress  in  a  plate  girder 
tends  to  cause  the  flange  angles  to  slide  on 
the  web.  In  finding  this  stress,  it  is  custom¬ 
ary  to  consider  a  section,  such  as  r  r.  Fig.  4, 
made  between  the  flange  angles  and  the  web;  this  section  cuts 


DESIGN  OF  PLATE  GIRDERS 


15 


only  the  rivets  that  connect  the  vertical  leg’s  of  the  flange 
angles  to  the  web.  The  longitudinal  shearing  stress  on  the 
section  rr,  per  unit  of  length,  is  found  by  the  formula  in  Art.  9, 

VG 


V  = 


/ 


In  this  case,  G  is  simply  the  static  moment  of  the  flange 


about  the  neutral  axis,  or 


A  h. 


Substituting  this  value  for  G, 


and  using  the  value  of  /  found  in  Art.  4,  the  formula  becomes 


Si'  = 


v\ 

Ah;  th 3 
2  +  16 


or,  neglecting  in  the  denominator  the  term 

Ak 2 

very  small  compared  with  — —— , 

z 


th * 
16’ 


which  is 


s  i 


t  — 


y(Ahg 


Ah; 


V 


If  the  pitch  of  the  flange  rivets  is  p ,  then,  since  the  longi¬ 
tudinal  shear  per  unit  of  length  is  sj,  the  stress  K  that  is 

V 


transmitted  by  one  rivet  is  psG  or  pX 


In  computing 


rivet  pitch,  K  is  the  value  of  one  rivet.  We  have,  therefore, 

K  =  —  -  (1) 


and 


P  = 


Kht 

V 


(2) 


As  hs  does  not  materially  differ  from  the  distance  h , 
between  the  rivet  lines  in  the  vertical  legs  of  the  flange 
angles,  it  is  the  general  practice,  and  one  that  will  be  fol¬ 
lowed  in  this  Course,  to  replace  hs  by  hr  in  the  preceding 
formulas.  Those  formulas  then  become 

K  =  *V- 


P  = 


K 

Khr 

V 


(3) 


(4) 


L6 


DESIGN  OF  PLATE  GIRDERS 


§75 


The  distance  hr  is  always  less  than  hg)  and  so  formula  4 
gives  a  smaller  pitch  than  is  actually  required;  that  is,  the 
error  is  on  the  side  of  safety. 

Example  1.— At  a  given  section  of  a  plate  girder,  the  maximum 
vertical  shear  is  72,000  pounds;  the  distance  between  the  rivet  lines  of 
the  flanges  is  27  inches;  and  the  pitch  of  the  flange  rivets  is  3  inches. 
How  much  stress  is  transmitted  by  each  rivet? 


Solution. — Substituting  the  given  values  in  formula  3, 
K  =  -  X  ^,QQQ  =  8,000  lb.  Ans. 


Example  2.— The  maximum  vertical  shear  at  a  given  section  of  a 
plate  girder  is  150,000  pounds;  the  value  of  a  flange  rivet  is  9,600 
pounds;  and  the  vertical  distance  between  the  rivet  lines  of  the  flanges 
is  37.5  inches.  What  is  the  required  pitch  of  the  rivets? 


Solution.— To  use  formula  4,  we  have  V  =  150,000  lb.,  hr  =  37.5 in., 
and  K  =  9,600  lb.  Substituting  these  values  in  the  formula,  we  have 

9,600  X  37.5 


P  = 


150,000 


=  2.4  in.  Ans. 


EXAMPLES  EOR  PRACTICE 

1.  The  maximum  vertical  shear  at  a  given  section  of  a  girder  is 
240,000  pounds.  The  width  of  web  is  64  inches,  and  the  thickness  is 
■Yq  inch.  What  is  the  maximum  intensity  of  shearing  stress? 

Ans.  6,667  lb.  per  sq.  in. 

2.  The  maximum  vertical  shear  at  a  given  section  of  a  girder  is 
100,000  pounds.  If  the  width  of  web  is  36  inches,  and  the  clear 
unsupported  distance  is  24  inches,  what  thickness  must  be  used  in 

order  that  the  intensity  of  shearing  stress  shall  not  exceed  — — ? 

1H - — — 

/  ^  3,000 1* 

Ans.  y  in- 

3.  The  maximum  vertical  shear  at  a  given  section  of  a  plate  girder 

is  102,000  pounds;  the  distance  between  the  rivet  lines  of  the  flanges  is 
34  inches;  and  the  pitch  of  the  flange  rivets  is  2.5  inches.  How  much 
stress  is  transmitted  by  each  rivet?  Ans.  7,500  lb. 

4.  The  maximum  vertical  shear  at  a  given  section  of  a  plate  girder 

is  178,200  pounds;  the  value  of  a  flange  rivet  is  10,800  pounds;  and  the 
vertical  distance  between  the  rivet  lines  of  the  flanges  is  49.5  inches. 
What  is  the  required  pitch  of  rivets?  Ans.  3  in. 


§75 


DESIGN  OF  PLATE  GIRDERS 


17 


GENERAL  DESIGN 

14.  Deck  and  Half-Through  Girder  Bridges. — -The 
design  of  a  plate  girder  requires  the  calculation  of  the  maxi¬ 
mum  shears  and  moments  at  several  sections  along  the  girder. 

In  a  half-through  plate-girder  bridge,  the  load  is  applied 
to  the  girders  at  the  panel  points,  and  it  is  simply  necessary 
to  calculate  the  maximum  bending  moment  at  each  panel 
point,  and  the  maximum  shear  in  each  panel.  The  bending 
moment  may  be  assumed  to  vary  uniformly  between  panel 
points;  that  is,  the  part  of  the  moment  curve  between  two 
panel  points  may  be  assumed  to  be  straight.  The  shear  in 
each  panel  may  be  assumed  constant  between  panel  points; 
then,  the  intensity  of  the  shearing  stress  and  the  rivet  pitch 
will  be  constant  in  each  panel,  but  will  change  at  each  panel 
point. 

In  a  deck,  plate-girder  bridge,  the  load  is  applied  at  every 
point  throughout  the  length  of  the  girder,  and  it  is  necessary  to 
compute  the  maximum  moments  and  shears  at  several  sections 
along  the  girder;  for  convenience,  these  sections  are  usually 
taken  from  5  to  10  feet  apart.  From  the  values  so  found, 
the  intensity  of  the  shearing  stress,  the  rivet  pitch,  and  the 
required  flange  areas  at  the  different  sections  are  found  by 
means  of  the  formulas  already  given.  The  values  at  inter¬ 
mediate  sections  can  then  be  found  by  means  of  a  curve 
similar  to  the  curve  of  flange  areas. 

i 

15.  Girders  With  Curved  and  Inclined  Flanges. 

The  same  formulas  are  used  for  girders  with  curved  or 
inclined  flanges  as  for  those  with  parallel  flanges.  As,  how¬ 
ever,  the  height  of  the  girder  is  different  at  different  sections, 
the  width  of  the  web  h,  and  the  vertical  distance  hg  between 
the  centers  of  gravity  of  the  flanges,  must  be  calculated  at 
each  section  at  which  the  flange  area,  intensity  of  shearing 
stress,  or  rivet  pitch  is  required.  The  results  will  be  true  for 
the  horizontal  flange,  and  for  all  practical  purposes  near 
enough  to  the  true  results  for  the  inclined  flange,  unless  the 
angle  between  the  inclined  flange  and  the  horizontal  is  greater 


18 


DESIGN  OF  PLATE  GIRDERS 


75 


than  about  10°.  In  the  latter  case,  the  required  area  of  sec¬ 
tion  of  the  inclined  flange  at  any  section  may  be  found  by 

multiplying  the  area  as  found  by  the  formula  A  —  —  ~ 

s  hg  8 

(Art.  5)  by  the  secant  of  the  angle  between  the  inclined 
flange  and  the  horizontal.  The  other  values  are  close  enough 
for  all  practical  purposes. 

16.  Girders  With  Vertical  Flange  Plates  and 
Secondary  Flange  Angles. — In  long  girders  in  which 
the  flanges  must  be  very  large,  it  is  advisable  to  make  use 
of  a  modified  type  of  flange  in  order  to  avoid  having  a  great 
thickness  of  flange  plates,  and  consequently  an  excessive 


mmmmm  mmi 

.  — — " 

1 

d 

1 

ft  __ 

r  n 

L  II 

Q  Q  Q  Q 

O  Q  O  O  Q 

Q  O  O  Q 

Q  Q  Q  Q  Q 

e' 

(a) 

6  ^ 

(» 

t 

(c) 

Fig.  5 


grip  for  the  rivets.  The  modified  flange  usually  has  one  of 
the  forms  shown  in  Fig.  5  ( a ),  ( b ),  and  (c) .  In  Fig.  5  ( a ), 
vertical  flange  plates  d ,  d,  each  of  which  has  a  width  about 
twice  that  of  the  flange  angle,  are  inserted  between  the  flange 
angles  and  the  web.  In  Fig.  5  {b) ,  there  are,  in  addition  to 
the  vertical  flange  plates,  secondary  flange  angles  e,  e  riveted 
to  the  flange  plates  below  the  main  flange  angles-  In 
Fig.  5  (<:),  the  secondary  flange  angles  are  used  and  are 
riveted  to  the  web,  the  vertical  flange  plates  being  omitted. 
The  secondary  flange  angles  are  sometimes  placed  with  the 
outstanding  leg  below,  as  shown  in  full  lines,  and  sometimes 
with  it  above,  as  shown  by  dotted  lines  in  Fig.  5  (c) .  The 
design  of  a  girder  with  flanges  as  represented  in  Fig.  5  makes 
use  of  no  new  principle;  the  formulas  and  methods  that  have 
been  explained  in  the  preceding  articles  are  used.  In  calcu¬ 
lating  the  location  of  the  center  of  gravity  of  the  flange, 


§75 


DESIGN  OF  PLATE  GIRDERS 


19 


the  vertical  plates  and  secondary  angles  must  be  taken  into 
consideration. 

17.  The  vertical  plates,  as  well  as  the  main  flange  angles, 
are  continued  the  entire  length  of  the  girder;  the  secondary 
flange  angles  are  usually  stopped  where  they  are  no  longer 
required.  To  find  the  required  length  of  flange  members, 
the  curve  of  flange  areas  is  used  as  represented  in  Fig.  6. 


The  value  ~  is  first  laid  off  on  Y  O  Y'  above  and  below  AO  A'; 

then  the  area  of  the  two  vertical  flange  plates;  then  that  of 
the  two  main  flange  angles;  then  the  first  flange  plate;  then 
the  secondary  flange  angles;  and  then  the  remaining  flange 
plates,  in  order.  _ 

SPLICES 

18.  Lengths  of  Members. — The  web  and  the  flange 
members  require  to  be  spliced  when  they  are  longer  than  the 
lengths  given  in  Table  V.  Web-plates  are  generally  made 
as  long  as  possible.  Flange  plates  are  made  narrower  than 


20 


DESIGN  OF  PLATE  GIRDERS 


§75 


web-plates,  and  can  be  procured  in  greater  lengths;  angles  also 
can  be  procured  in  great  lengths,  in  many  cases  as  long  as 

% 

100  feet.  Owing  to  practical  difficulties  in  handling  long  slen¬ 
der  pieces,  however,  it  is  usually  specified  that  all  flange  mem¬ 
bers  shall  be  spliced  when  they  are  longer  than  about  70  feet. 


19.  Web  Splices. — The  different  portions  of  which  the 
web  is  composed  are  made  the  full  height  of  the  girder  and 
rectangular,  with  the  ends  at  right  angles  to  the  flanges. 
The  ends  of  two  consecutive  portions  are  placed  together  and 
covered  by  plates,  called  splice  plates,  on  each  side.  These 
plates  are  riveted  to  the  ends  of  the  portions  of  the  web  in  the 
manner  represented  in  Fig.  7  (a) ,  in  which  A  B  is  the  section  at 
which  the  web  is  spliced,  and  the  plate  CD  is  one  of  the  splice 
plates.  The  flange  angles  assist  somewhat  in  splicing  the  web, 
but  it  is  customary  to  ignore  their  effect,  and  to  design  the 
splice  on  the  assumption  that  the  web  is  spliced  entirely  by 
the  splice  plates,  and  to  make  the  splice  as  strong  as  the  web. 

If  the  splice  is  designed  to  resist  the  same  bending  moment 
as  the  web,  there  will  be  no  necessity  to  calculate  the  shear 
on  the  joint,  as  the  joint  will  always  be  strong  enough  in  shear. 
The  bending  moment  M  that  the  web  can  bear,  sometimes 
called  the  resisting;  moment,  is  given  by  the  formula 

tjr_ 

M  _  s_I_  _  _ _ 16_  _  sth2 

c  h  8 

2 


using  for  the  moment  of  inertia  the  approximate  value 


th 3 
16 


(see  Art.  4).  If  represents  the  height  and  h  the  com¬ 
bined  thickness  of  the  two  splice  plates,  one  on  each  side  of 
5  tt  hi 
8 


the  web, 


represents  the  combined  resisting  moment  of 


the  two  splice  plates.  In  order  that  they  may  have  the  same 
resisting  moment  as  the  web,  we  must  have 


s  t !  h2  _  5 t  h2  % 
~8~  “  ”  8  ’* 


whence 


§75 


DESIGN  OF  PLATE  GIRDERS 


21 


By  means  of  this  formula,  the  required  thickness  of  the 
splice  plates  can  be  found.  It  is  seldom  necessary,  however, 
to  compute  the  required  thickness;  it  is  generally  specified 
that  each  plate  shall  have  a  sectional  area  at  least  75  per 
cent,  that  of  the  web,  in  which  case  there  is  invariably 
sufficient  section. 

20.  Resisting  Moment  of  Web-Splice  Rivets. — The 
stress  in  the  web  is  transmitted  to  the  splice  plates  by  ver¬ 
tical  rows  of  rivets.  In  Fig.  7  ( a ),  two  vertical  rows  trans- . 
mit  the  stress  to  the  splice  plates  on  one  side  of  the  splice, 


A 


and  two  rows  transmit  the  stress  from  the  splice  plates  on 
the  other  side.  The  rivets  on  each  side  of  the  splice  must 
have  the  same  resisting  moment  as  the  web.  The  intensity 
of  stress  due  to  bending  varies  uniformly  as  the  distance 
from  the  neutral  axis;  in  like  manner,  the  amount  of  stress 
transmitted  by  a  rivet  varies  as  its  distance  from  the  neutral 
axis,  being  greatest  for  the  rivet  whose  distance  from  the 
neutral  axis  is  greatest,  as  represented  in  Fig.  7  ( b ).  If  K 
represents  the  stress  on  one  outside  rivet,  at  a  distance  r0 

from  the  neutral  axis,  then  Kx  —  K  X  — 1  represents  the 

r0 

,  \_»  Jf  Sa'  V 

stress  on  any  other  rivet  at  a  distance  rx  from  the  neutral 


22 


DESIGN  OF  PLATE  GIRDERS 


§75 


axis.  The  resisting  moment  of  a  rivet  is  the  product  of  the 
stress  on  the  rivet  and  its  distance  from  the  neutral  axis,  as 
K r0 ,  rlf  K 2  r2,  etc.  Expressing  the  stress  on  each  rivet  in 
terms  of  K,  the  resisting  moments  of  the  rivets  are 

r. 


K\  r,  =  K  r'-  r,  =  K  r' 

To 


2  Kr?  . 

-,  K 2  ra  = - ,  etc. 


K  r0  = 

r0  r0  r0  r0 

Therefore,  for  the  combined  resisting  moment  Mr  of  all 
the  rivets  on  one  side  of  the  splice,  we  have 

K 


M, 


Kr:  +  Krl  +  KrS  +  > 


.  =  —  (r07  +  rS+  ra’+  .  .  .) 

r0 

or,  denoting  by  Z  r1  the  sum  r0 5  +  r*  +  ?%  +  •  •  •  of  the 
squares  of  the  distances  r0,  rlf  r2,  etc., 


r0  r0  r0 
v 


Mr  =  .  (1) 

r*  i 

It  should  be  clearly  understood  that,  in  applying  this 
formula,  the  distance  of  every  rivet  from  the  neutral  axis 
should  be  squared,  and  the  results  added.  When  several 
rivets  are  at  the  same  distance  from  the  neutral  axis,  as  is 
the  case  when  rivets  are  arranged  in  horizontal  rows,  or 
when  some  rivets  are  as  far  above  as  others  are  below  the 
neutral  axis,  the  work  is  much  simplified  by  squaring  that 
distance  and  multiplying  the  result  by  the  number  of  rivets 
to  which  the  distance  is  common.  Thus,  in  Fig.  7  (a),  each 
distance,  as  r,,  is  common  to  four  rivets,  two  above  and  two 
below  the  neutral  axis.  In  this  case, 

2V  =  4(r0a  +  r12  +  r2J  +  .  .  .) 

In  order  that  the  splice  rivets  may  have  sufficient  strength, 
the  value  of  Mr  must  be  at  least  as  great  as  the  resisting 
moment  of  the  web,  and  K  must  not  exceed  the  value  of  the 
outside  rivet.  We  must,  therefore,  have 

-x.v  =  ^  (2) 

s  r0  o 

In  applying  this  formula,  it  is  customary  to  assume  first  a 
spacing  of  rivets  and  calculate  their  resisting  moment.  If 
the  value  is  not  sufficient,  more  rivets  are  added,  either  by 
spacing  the  rivets  closer  together,  or  by  adding  another 
row  outside  of  the  first  two.  For  this  purpose,  the  arrange¬ 
ment  represented  in  Fig.  8  is  frequently  employed,  the 


§75 


DESIGN  OF  PLATE  GIRDERS 


23 


advantage  being  that  most  of  the  rivets  are  near  the  flanges, 
where  the  value  of  the  resisting  moment  is  greatest.  The 
thickness  of  these  plates  may  be 
found  by  means  of  the  formula 

tx  —  t  X  “  (Art.  19),  substi- 
hx 

tuting  for  //,  the  sum  of  the 
heights  of  the  three  portions  of 
the  splice  plate;  the  thickness  on 
each  side,  however,  is  usually 
made  about  75  per  cent,  of  that 
of  the  web. 

Example. — If  the  plate  girder 
represented  in  Fig.  8  has  a  web 
72  in.  X  g-  in.,  spliced  with  §-inch 
rivets  and  splice  plates  as  shown, 
what  is:  (a)  the  required  thickness 
of  splice  plates  on  each  side?  ( b )  the 
resisting  moment  of  the  rivets  on  each  side  of  the  splice,  assuming 
the  value  of  a  rivet  to  be  9,600  pounds? 

Solution. — ( a )  As  the  splice  plates  are  made  up  of  three  parts  on 
each  side  of  the  web,  the  value  of  hx  is  14  -f  3l|-  +  14  =  59.5  in. 
Then,  since  t  is  .5  and  h  is  72  in., 

tx  —  .5  X  rTTTa  =  *5  X  1.46  =  .  /3  in. 

59.5  'i 

for  both  sides,  or  .73  4-  2  =  .365  in.  (say  f  in.)  for  each  side.  Ans. 

(b)  The  distances  of  the  rivets  from  the  neutral  axis  are  2,  6,  10, 
14,  17^,  21,  24^,  and  28  in.,  respectively.  There  are  four  rivets  at  each 
of  the  first  four  distances,  and  eight  rivets  at  each  of  the  last  four. 
To  apply  formula  1,  we  have  K  —  9,600  lb.,  r  =  28  in.,  and 
IV  =  4  X  (22  +  62  +  102  +  142)  +  8  X(17.52  +  212  +  24.52  +  282)=  18,396 

Therefore, 

Mr  =  X  18,396  =  6,307,200_in.-lb.  Ans. 

21.  Flange-Angle  Splices. — Flange  angles  are  spliced 
by  riveting  angles  to  them,  as  represented  in  Fig.  9.  In 
this  figure,  (a)  is  the  elevation  of  a  portion  of  the  bottom 
flange,  (b)  is  the  cross-section  at  B  B,  and  (c)  is  the  plan  of 
the  flange  and  a  cross-section  at  C  C.  The  angles  d  are  the 
flange  angles,  the  angles  e  are  the  splice  angles,  and  the  line  / 
is  the  section  at  which  the  flange  angle  is  spliced.  Practice 


24 


DESIGN  OF  PLATE  GIRDERS 


§75 


varies  as  to  the  method  of  designing  a  flange-angle  splice. 
Some  engineers  use  one  splice  angle  riveted  to  the  flange 
angle  that  is  spliced;  this  is  open  to  the  objection  that  the 
splice  angle  must  be  very  long  in  order  to  get  sufficient 
rivets  to  develop  the  stress,  and  therefore  interferes  with 
other  details,  such  as  stiffeners.  Others  use  two  angles,  as 
in  Fig.  9,  and  assume  that  the  stress  in  the  flange  angle  is 
equally  divided  between  the  two.  On  account  of  the  fact 
that  the  angle  on  the  side  opposite  the  splice  gets  its  stress 
through  the  web  and  the  other  flange  angle,  it  is  probable 
that  the  angle  in  contact  with  the  flange  angle  that  is  spliced 


d 


B 


O 


Q  Q 
e  Q  Q 


Q 


f  o 

Q 


O 


Q 


O 


O 


(a) 


B 


^ d 

O 

O  Q  Q  Q  Q  Q 

Q  Q  Q  Q  Q  Q 

o 

O 

- — - — - 1 - - - 

O  Q  Q  r/  O  Q  o 
'e  O  O  Q  i  O  Q  Q 

i  . 

Q 

(c) 


Fig.  9 


gets  somewhat  more  than  one-half  the  stress.  The  assump¬ 
tion  most  frequently  made  is  that  the  splice  angle  in  contact 
with  the  flange  angle  that  is  spliced  takes  three-quarters  of 
the  stress;  this  angle  is  designed  on  this  basis  to  have  a 
cross-section  three-quarters  that  of  the  flange  angle,  and 
made  long  enough  to  get  sufficient  rivets  on  each  side  of  the 
splice  to  transmit  three-quarters  of  the  stress.  The  other 
splice  angle  is  then  made  the  same  size  and  length.  If  FA  is 
the  area  of  section  (net  area  for  tension,  gross  area  for  com¬ 
pression)  of  one  flange  angle,  then  the  area  FJ  of  section  of 
each  splice  angle  is  given  by  the  formula 

Fa>  =  ,75  Fa  (1) 


§75 


DESIGN  OF  PLATE  GIRDERS 


25 


If  is  the  allowable  intensity  of  bending-  stress,  the  total 
stress  in  the  flange  angle  is  FAs ,  and  in  the  splice  angle, 
.75  Fas.  The  number  n  of  rivets  in  the  splice  angle  on  each 
side  of  the  splice  is  given  by  the  formula 


n 


.75  Fas 
K  " 


(2) 


in  which  K  is  the  value  of  one  rivet.  Splice  angles  are  cut 
from  angles  having  legs  the  same  width  as  the  flange  angles, 
so  that  the  edges  of  splice  and  flange  angles  will  be  even, 
and  not  as  shown  by  dotted  lines  in  Fig.  .9  ( b ).  The  area  of 
cross-section  of  such  an  angle  can  be  found  by  deducting 
from  the  area  given  in  Tables  IX  and  X  for  the  original 
angle  the  amount  that  is  sheared  off. 


Example. — The  flange  angles  in  the  tension  flange  of  a  plate  gir¬ 
der  are  6  in.  X  6  -in.  X  \  in.,  and  the  allowable  intensity  of  stress  is 
16,000  pounds  per  square  inch.  The  diameter  of  the  rivets  is  •§■  inch. 
(a)  What  size  of  splice  angle  must  be  used  if  the  angle  is  spliced  as 
represented  in  Fig.  9?  (b)  If  the  value  of  one  rivet  is  5,000  pounds, 

how  many  rivets  are  required  on  each  side  of  the  splice? 


Solution. — ( a )  The  area  of  a  6"  X  6"  X  angle  is  5.75  sq.  in. 
As  we  are  considering  the  tension  flange,  the  net  section  is  required; 
as  there  are  two  rivet  holes  in  each  section,  and  the  area  of  a  hole  for 
a  -g-inch  rivet  is  .5  sq.  in.,  as  given  in  Table  XXVII,  the  net  section 
is  5.75  —  2  X  .5  =  4.75  sq.  in.  (=  Fa).  The  required  net  area  Fa'  of 
one  splice  angle  is,  then,  by  formula  1,  .75  X  4.75  =  3.56  sq.  in.  As 
the  flange  angle  is  %  in.  thick,  -g-  in.  must  be  sheared  off  each  leg  of 
each  splice  angle.  The  thinnest  6"  X  6"  angle,  which  is  f-  in.  thick, 
will  be  tried  first.  The  area  of  this  angle,  as  given  in  Table  IX,  is 
4.36  sq.  in.;  if  ^  in.  is  cut  from  each  leg,  the  area  is  reduced  by 
2  X  .5  X  .375  =  .37  sq .  in . ,  nearly.  As  there  are  two  holes  in  each  angle, 
the  area  will  be  still  further  reduced  by  2  X  .375  =  .75  sq.  in.  Then, 
the  net  area  of  one  angle  5^-  in.  X  5^-  in.  X  |  in.  will  be  4.36  —  .37  —  .75 
=  3.24  sq.  in.  As  3.56  sq.  in.  is  required,  this  is  not  enough.  The 
next  size,  6  in.  X  6  in.  X  tq  in.,  the  gross  area  of  which  is  5.06  sq.  in., 
will  be  tried.  If  \  in.  is  sheared  from  each  leg,  the  area  is  reduced 
by  2  X  .5  X  .44  =  .44  sq.  in.  The  two  rivet  holes  still  further  reduce 
the  section  by  2  X  .44  =  .88  sq.  in.  Then,  the  net  area  of  one  angle 

in.  X  5|-  in.  X  -fe  in.  is  5.06  —  .88  —  .44  =  3.74  sq.  in.,  which  is 
sufficient.  Ans. 

(b)  The  total  stress  in  one  flange  angle  is  4.75  X  16,000  =  76,000  lb., 
and  the  portion  to  be  transmitted  by  the  rivets  is  three-fourths  of  this, 


26  DEwSIGN  OF  PLATE  GIRDERS  §75 

or  57,000  lb.  Then,  the  required  number  of  rivets  is  57,000  -4-  5,000 
=  11.4,  or,  say,  12  rivets  on  each  side  of  the  splice. 

22.  Flange-Plate  Splices. — Flange  plates  are  spliced 
either  by  additional  plates,  or  by  continuing  the  outer  plates 
beyond  their  theoretical  ends  a  sufficient  distance  to  splice 
the  plates  below  them.  The  plates  nearest  the  flange  angles 
are  the  longest,  and  are  the  ones  that  require  to  be  spliced. 

23.  Additional  Splice  Plates. — In  the  first  method  of 
splicing,  the  joint  in  the  plate  that  is  to  be  spliced  is  usually 


located  somewhere  near  the  center  of  the  girder,  as  repre¬ 
sented  at  /,  Fig.  10,  and  a  splice  plate  g  of  the  same  thick¬ 
ness  as  the  flange  plate  is  riveted  to  the  outside  of  the  flange. 
The  splice  plate  is  made  long  enough  to  contain  sufficient 
rivets  on  each  side  of  the  joint  to  properly  transmit  the 
stress  from  one  part  of  the  flange  plate  to  the  other.  The 
number  of  rivets  that  is  required  to  transmit  the  stress  to  or 
from  the  splice  plate  can  be  found  by  dividing  the  stress  by 
the  value  of  one  rivet;  the  latter  will  usually  be  the  value  in 
single  shear.  When,  as  in  Fig.  10,  there  are  intermediate 


§75 


DESIGN  OF  PLATE  GIRDERS 


27 


plates  between  the  splice  plate  and  the  plate  that  is  spliced, 
there  is  some  uncertainty  as  to  how  the  stress  is  carried 
around  the  joint;  to  provide  for  this,  the  number  of  rivets  in 
the  splice  plate  is  increased  as  specified  in  Arts.  61  and  134 
of  B.  S.  In  the  present  case,  since  there  are  three  interme¬ 
diate  plates,  the  number  of  rivets  will  be  increased  3  X  20 
=  60  per  cent.  Any  flange  plate  may  be  spliced  in  the 
same  way. 

24.  Continuing  Outer  Plates. — In  the  second  method 
of  splicing,  the  location  of  the  joint  in  the  plate  that  is  to  be 
spliced  is  found  by  means  of  the  curve  of  flange  areas.  In 
Fig.  10,  the  curve  of  flange  areas  and  one-half  of  the  flange 
are  laid  out  to  the  same  horizontal  scale;  the  points  d ,  c , 
and  b  are  the  theoretical  ends  of  the  three  outside  flange 
plates,  and  it  is  desired  to  splice  the  first  flange  plate.  The 
ordinate  O  I'  represents  the  flange  area  as  found  by  the 

formula^  =  -^-(Art.  6),  and  01  represents  the  actual  area 
she 

of  flange.  From  /,  IE  is  laid  off  to  scale  to  represent  the 
area  of  the  plate  that  is  to  be  spliced;  the  line  EE'  is  drawn 
parallel  to  X'OX  to  its  intersection  E'  with  the  curve,  and 
the  line  E'  e  is  drawn  perpendicular  to  X'OX.  Then,  e'  E' 
represents  the  entire  area  of  flange,  exclusive  of  the  plate  a ; 
that  is,  if  all  the  plates  are  carried  beyond  e,  the  first  plate  a 
can  be  spliced  at  that  section.  For  this  purpose,  the  outer 
plate,  instead  of  being  stopped  at  d}  is  carried  beyond  e ,  as 
represented  by  the  dotted  lines.  As  there  is  no  stress  in  the 
first  flange  plate  a  at  the  section  e ,  and  there  is  full  stress  in 
the  outer  plate  d ,  it  remains  to  find  how  many  rivets  must 
be  contained  in  the  plate  d  beyond  e,  in  order  to  transmit  its 
stress  to  a ;  this  is  found  by  dividing  the  stress  in  the  out¬ 
side  plate  by  the  value  of  one  rivet  in  single  shear.  In  the 
present  case,  as  there  are  two  plates  between  d  and  a ,  the 
required  number  of  rivets  will  be  2  X  20  =  40  per  cent, 
greater  than  the  theoretical  number.  The  plate  d  will  be 
continued  to  a  point  d\  the  distance  e  d'  being  made  such 
that  there  will  be  sufficient  room  for  the  required  number 


28 


DESIGN  OF  PLATE  GIRDERS 


75 


of  rivets.  In  a  similar  manner,  any  flange  plate  may  be 
spliced. 

It  will  seldom  be  found  necessary  to  splice  any  flange 
plate  at  more  than  one  section,  nor  more  than  two  plates  in 
any  flange.  When  two  plates  must  be  spliced,  the  first  plate 
can  be  spliced  at  one  end  of  the  girder,  as  at  e ,  Fig.  10,  and 
the  second  plate  at  a  corresponding  point  on  the  other  side 
of  the  center. 

Example. — Let  Fig.  10  represent  the  top  flange  of  a  plate  girder 
in  which  the  allowable  intensity  of  stress  is  16,000  pounds  per  square 
inch,  and  the  sizes  of  the  plates  are  as  follows:  a,  16  in.  X  \  in.; 
b,  16  in.  X  \  in.;  c,  16  in.  X  yq  in.;  and  d,  16  in.  X  -f  in.  (a)  If  it  is 
desired  to  splice  plate  a  at  section  j,  what  is  the  required  size  of  the 
splice  plate  g?  ( b )  If  the  value  of  one  rivet  in  single  shear  is  6,600 
pounds,  how  many  rivets  must  be  included  in  plate  g?  ( c )  If  it  is 
desired  to  splice  plate  a  at  section  e ,  how  many  rivets  must  be  included 
in  plate  d  between  e  and  d',  assuming  the  value  of  one  rivet  to  be 
6,600  pounds? 

Solution. — (a)  As  plate  g  is  an  additional  splice  plate,  it  must  be  the 
same  size  as  the  plate  that  is  to  be  spliced,  that  is,  16  in.  X  1  in.  Ans. 

(b)  The  area  of  cross-section  of  plate  g  is  8  sq.  in.,  and,  since  the 
intensity  of  stress  is  16,000  lb.  per  sq.  in.,  the  stress  in  plate  g  is 
8  X  16,000  =  128,000  lb.  As  the  value  of  one  rivet  in  single  shear 
is  6,600  lb.,  the  number  of  rivets  required  to  transmit  this  stress  to 
plate  g  is  128,000  -r-  6,600  =  19.4.  Since  there  are  three  intermediate 
plates  between  g  and  a,  the  number  must  be  increased  3  X  20  =  60 
per  cent.  Then,  the  total  number  of  rivets  required  on  each  side  of  /  is 

19.4  +  yyo  X  19.4  =  31 

As  the  flange  rivets  in  the  plates  are  driven  in  pairs,  it  is  necessary 
to  have  32  rivets.  Ans. 

(c)  The  area  of  cross-section  of  plate  d  is  16  in.  X  f  in.  =6  sq.  in.; 
and,  since  the  intensity  of  stress  is  16,000  lb.  per  sq.  in.,  the  stress  in 
plate  d  is  6  X  16,000  =  96,000  lb.  As  the  value  of  one  rivet  is  6,600  lb., 
the  number  of  rivets  required  to  transmit  the  stress  to  the  plate  d  is 
96,000  -7-  6,600  =  14.5  rivets.  Since  there  are  two  intermediate  plates 
between  d  and  a ,  the  number  must  be  increased  2  X  20  =  40  per  cent. 
Then,  the  total  number  of  rivets  required  in  plate  d  between  d'  and  e  is 

14.5  +  ^X  14.5  =  20.3 

As  this  is  so  close  to  20,  20  rivets  will  be  sufficient,  although  it  is 
better  to  use  22.  Ans. 

25.  Splices  in  Secondary  Flange  Angles  and  Verti¬ 
cal  Flange  Plates. — Secondary  flange  angles  are  usually 


§75 


DESIGN  OF  PLATE  GIRDERS 


29 


Q 

O 

Q 

Q 

O 

O 

O 

Q 

Q 

Q 

O 

Q 

O 

O 

O 

O 

Q 

0) 

a 

Q 

Q 

O 

Q 

O 

O 

O 

1 

Q 

O 

O 

Q 

O 

O 

O 

O 

P 

O 

 1 

• - - — 1 

Fig.  11 


spliced,  as  represented  in  Fig.  11,  by  means  of  one  splice 
angle  riveted  to  the 
inside  of  the  flange 
angle  and  a  splice 
plate  having  a  width 
about  the  same  as 
that  of  the  flange 
angle,  riveted  to  the 
back  of  the  latter. 

The  area  of  the  splice 
angle  is  made  about 
75  per  cent,  and  that 
of  the  splice  plate 
about  25'  per  cent,  that  of  the  flange  angle,  the  area  of  the 

two  together  being 
not  less  than  the  area 
of  the  flange  angle. 

Vertical  flange 
plates  are  spliced, 
as  represented  in 
Fig.  12,  by  means  of 
one  vertical  splice 
plate  riveted  to  the 
vertical  legs  of  the 
flange  angles  on  the 
same  side  of  the  web 
as  the  vertical  plate  that  is  spliced.  The  area  of  the  splice 

i 

plate  is  made  not  less  than  that  of  the  flange  plate. 


O 

O  Q  Q 

Q>  0  a 

O 

O 

Q  Q  Q  Q 

OOOO 

O 

Q 

Q  _Q  Q 

Q  Q  Q 

O 

Q 

O  Q  O  O 

O  O  Q  Q 

1 — — 

S/?//ce  Pfaf&' 


Fig.  12 


EXAMPLES  FOR  PRACTICE 

1.  What  is  the  resisting  moment  of  a  36"X  -f"  web,  if  the  maximum 
intensity  of  the  bending  stress  is  16,000  pounds  per  square  inch? 

Ans.  1,620,000  in. -lb. 

2.  If  the  web  represented  in  Fig.  7  is  70  inches  wide  and  inch 
thick,  what  is  the  required  thickness  of  splice  plate  on  each  side,  assu¬ 
ming  the  height  to  be  57.5  inches?  Ans.  yq  hi.  thick  on  each  side 

3.  If  the  rivets  in  Fig.  7  are  spaced  as  shown  at  the  left-hand  side, 

and  the  value  of  one  rivet  is  10,800  pounds,  what  is  the  resisting 
moment  of  the  rivets  in  the  splice?  Ans.  3,849,600  in. -lb. 

135—8 


30 


75 


DESIGN  OF  PLATE  GIRDERS 

4.  The  flange  angles  in  the  compression  flange  of  a  plate  girder  are 
8  in.  X  8  in.  X  f  in.,  and  the  allowable  intensity  of  stress  is  16,000 
pounds  per  square  inch,  (a)  What  size  of  splice  angle  must  be  used? 
(b)  If  the  value  of  one  rivet  is  6,600  pounds,  how  many  rivets  are 
required  in  the  splice”  angle? 

Ans  { ( a )  ^  angles,  8  in.  X  8in.  X  f  in.,  cut  to  7-y  in.  X  7^  in.  X  f  in. 

’  1  (b)  22  rivets  on  each  side  of  the  joint 

5.  (a)  If  the  vertical  flange  plate  in  Fig.  12  is  15  inches  wide  and 
inch  thick,  and  the  splice  plate  is  13  inches  wide,  what  is  the  required 

thickness  of  the  latter?  (b)  If  the  allowable  intensity  of  stress  is  16,000 
pounds  per  square  inch,  and  the  value  of  one  rivet  is  6,600  pounds, 
how  many  rivets  are  required  in  the  splice  plate? 

Ans.  {  M  t  in-  thick 

'  \  (b)  18  or  20  rivets  on  each  side  of  the  joint 


BEARINGS 

26.  Size  of  Bedplates. — The  end  of  a  girder,  where 
the  girder  rests  on  the  masonry  or  other  support,  must  be 


i 

u 


p- 


(c)  d 


© 

©  ©  0 

© 

© 

©  ©  ©  © 

© 

© 

© 

© 

© 

© 

0 

© 

/ 

© 

C  C 

© 

s 

0 

© 

© 

0 

© 

© 

© 

© 

© 

© 

© 

© 

© 

©  ©  ©  © 

0  \ 

© 

©  ©  © 

0 

© 

P 


(a) 


u 


l—O  :  ©“I 

jo  ©  ©  ©I 


(b) 

Fig.  13 


©|  ©  #  ©  I©; 
J© Ql  ' 


l©  © 

©  © 


n 


(b) 

Fig.  14 


strong  enough  to  resist  the  reactions.  The  required  area  of 


DESIGN  OF  PLATE  GIRDERS 


31 


a 


75 


bearing,  if  the  girder  rests  on  masonry,  is  found  by  dividing 
the  maximum  reaction  by  the  allowable  intensity  of  bearing  on 
the  masonry.  For  example,  if  the  reaction  is  200,000  pounds, 
and  the  allowable  intensity  of  bearing  is  500  pounds  per 
square  inch,  the  required  area  of  bearing  is  200,000  -f-  500 
=  400  square  inches.  Bedplates  are  usually  made  rect¬ 
angular  and  very  nearly  square;  in  the  present  case,  each  will 

need  to  be  about  v400  =  20  inches 
on  each  side. 


c 

\ 


Q  O/C'Q  Q 


P~ 


Q 


O 


Q 

O 

J2 


Q 

Q 


9 


O 


o 


Q  O 
Q 


d 


(a) 


ho 

p.^lVT 1 

(*>) 

Pig.  15 


V 


27.  End  Stiffeners. — The 
ends  of  plate  girders  are  stiffened 
by  stiffeners  at  each  end  of  the  bed¬ 
plates.  The  arrangements  usually 
employed  are  represented  in  Figs.  13, 

14,  and  15,  in  which  c,  c  are  the  stif¬ 
feners;  d ,  the  sole  plates;  and  e ,  the 
bedplates.  The  arrangement  rep¬ 
resented  in  Fig.  13  is  most  used, 
although  that  shown  in  Fig.  14  is 
somewhat  better  on  account  of  the 
fact  that  in  it  the  bearing  of  the 
stiffeners  is  not  so  close  to  the 
edge  of  the  bedplate;  the  pressure 
is  therefore  more  evenly  distributed 
over  the  area  of  the  bedplate.  In 
the  arrangement  represented  in 
Fig.  15,  the  additional  stiffeners  d 
are  added.  The  plates  g  are  called 
reinforcing  plates,  and  are  added  to  distribute  the  stress 
more  evenly  over  the  web. 


0-0  0 
O  0  o  o 


o 

o  o 


28.  D'i  stribiition  of  Reaction. — The  reaction  is 
assumed  to  be  equally  divided  among  the  end  stiffeners, 
and  evenly  distributed  over  the  area  of  the  outstanding  legs 
of  the  stiffeners  where  they  bear  on  the  upper  side  of  the 
lower  flange  angle.  The  length  of  the  portion  of  a  stiffener 
in  contact  with  the  lower  flange  angle  is  usually  about  i  inch 
less  than  the  nominal  width  of  the  outstanding  leg.  If  t'  is 


32 


DESIGN  OF  PLATE  GIRDERS 


§75 


the  thickness  of  a  stiffener  angle;  b ,  the  nominal  width  of  the 
outstanding  leg;  and  s6,  the  allowable  intensity  of  bearing  on 
the  end  of, a  stiffener,  the  stress  that  one  stiffener  can  resist 
is  t' \b  —  If  R  is  the  reaction  and  n  the  number  of  end 

stiffeners,  the  amount  of  pressure  that  is  transmitted  by 

each  stiffener  is  — ;  and,,  in  order  that  the  stiffener  may  be 

n 

sufficiently  strong,  the  following  equation  must  be  satisfied: 

/'(/.-  \)sb  =  K 
n 

From  this  equation,  we  have 

f  =  _ X _ , 

n  sb(b  —  i) 

from  which  the  required  thickness  of  the  stiffeners  can  be 
found.  The  nominal  width  of  leg  is  controlled  by  Arts.  55 
and  128  of  B.  S. 


29.  Rivets  and  Stiffeners. — The  stress  in  each  stif¬ 
fener  is  transmitted  to  the  web  by  means  of  rivets.  The 
required  number  of  rivets  in  a  stiffener  can  be  found  by 

dividing  the  stress  in  one  stiffener  by  the  value  of  a 

rivet  in  single  shear,  or  in  bearing  on  the  angle;  or,  since 
the  same  rivets  connect  two  opposite  angles,  by  dividing  the 


stress  in  two  stiffeners 


2  7? 


by  the  value  of  a  rivet  in  double 


\  n  / 

shear,  in  bearing  on  two  angles,  or  in  bearing  on  the  web, 
whichever  is  least.  In  practice,  it  is  considered  advisable 
to  transmit  the  greater  part  of  the  stress  in  the  stiffeners  to 
the  web  below  the  neutral  axis.  When  it  is  impossible  to 
get  sufficient  rivets  below  the  neutral  axis  in  four  stiffeners, 
as  in  Figs.  13  and  14,  more  stiffeners  are  used,  as  in  Fig.  15. 


30.  Crimped  Stiffeners. — Stiffeners  are  sometimes 
placed  in  contact  with  the  web,  and  the  ends  crimped;  that 
is,  bent  out  around  the  vertical  legs  of  the  flange  angles,  as 
represented  in  Fig.  13  (r).  This  arrangement  is  open  to  the 
objection  that  it  is  difficult  to  bend  the  angles  so  they  will  bear 
evenly  on  the  flange  angle,  especially  on  the  outstanding  leg. 


§75 


DESIGN  OF'  PLATE  GIRDERS 


33 


31.  Loose  Fillers. — The  best  practice  at  the  present 
time  is  to  make  the  stiffener  angles  straight  from  top  to 
bottom,  and  fill  in  the  space  between  them  and  the  web  by 
means  of  bars  the  same  width  as  the  adjacent  leg  of  the 
stiffener  and  the  same  thickness  as  the  flange  angles,  as 
represented  in  Figs.  13  and  14.  These  bars  are  called  loose 
fillers;  they  simply  serve  to  fill  the  space  between  the  angle 
and  the  web.  The  number  of  rivets  required  to  connect  the 
stiffener  to  the  web  must  be  increased  20  per  cent,  when  this 
form  of  filler  is  used. 


32.  Reinforcing:  Plates  or  Tight  Fillers. — The  filler 
under  the  stiffeners  in  Fig.  15  is  continued  under  all  the 
angles,  and  riveted  to  the  web  by  rivets  located  outside  of 
the  stiffeners.  The  filler  is  then  called  a  tight  filler,  or 
reinforcing  plate;  it  distributes  the  stress  over  the  area 
of  the  web.  Such  a  plate  is  not  to  be  considered  an  inter¬ 
mediate  plate,  but  rather  a  part  of  the  web,  as  it  is  firmly 
riveted  to ‘it,  and  in  calculating  the  bearing  value  of  the 
rivet  on  the  web  the  thickness  of  these  plates  must  be 
included. 


Example  1. — The  maximum  reaction  at  the  end  of  the  plate  girder 
represented  in  Fig.  13  is  135,000  pounds,  (a)  If  the  stiffeners  are 
5  in.  X  3^  in.,  and  the  allowable  intensity  of  bearing  is  18,000  pounds 
per  square  inch,  -what  is  the  required  thickness  of  the  stiffener  angles? 
(b)  If  the  value  of  one  rivet  in  single  shear  is  6,600  pounds,  in  bearing 
on  the  web,  10,800  pounds,  and  in  bearing  on  each  stiffener  angle, 
8,400  pounds,  how  many  rivets  are  required  to  connect  the  stiffeners 
to  the  web? 


Solution. — (a)  The  required  thickness  of  stiffeners  can  be  found 
by  the  formula  in  Art.  28, 

e  _ _ 

n  sb  ( b  -  |) 

In  the  present  case',  R  —  135,000,  n  =  4,  sb 
Substituting  these  values  in  the  formula  gives 

135,000 


18,000,  and  b  =  5. 


t<  = 


=  .42  in.,  or  in.,  nearly.  Ans. 


4  X  18,000  X  4.5 

( b )  The  rivets  that  connect  the  stiffeners  to  the  web  are  in  single 
shear  on  each  side  of  the  web,  and  in  bearing  on  the  yy-inch  stiffener 
angle.  Considering  first  the  stress  in  one  angle,  the  value  in  single 
shear  is  evidently  less  than  the  value  in  bearing  on  the  yV-inch  angle. 


34  DESIGN  OF  PLATE  GIRDERS  §75 

The  stress  in  each  stiffener  is  135,000  4-  4  =  33,750  lb.,  and  the  required 
number  of  rivets  is  33,750  4-  6,600  =  5.1. 

Considering  now  the  stress  in  two  angles,  the  rivets  are  in  double 
shear  at  2  X  6,600  =  13,200  lb.;  in  bearing  on  two  -pg-inch  angles,  at 
2  X  8,400  =  16,800  lb.;  and  in  bearing  bn  the  web,  at  10,800  lb.  The 
latter  value  being  the  smallest,  and  the  stress  in  two  stiffeners  being 
135,000-7-2  =  67,5001b.,  the  required  number  of  rivets  is  67,500  4- 10,800 
=  6.25.  This  number  is  larger  than  that  first  found,  and  must  be 
used.  As  there  are  loose  fillers  (see  Art.  31),  the  actual  number 
required  is 

6.25  +  ~!nPo  X  6.25  =  7.5,  say,  8  rivets.  Ans. 

Example  2. — The  maximum  reaction  at  the  end  of  the  plate  girder 
represented  in  Fig.  15  is  230,000  pounds;  the  thickness  of  web  is 

inch,  and  the  thickness  of  the  flange  angles  is  f-  inch.  Using  the 
working  stresses  given  in  Art.  29  of  B.  S. ,  it  is  desired  to  find:  (a)  the 
required  thickness  of  stiffeners,  if  the  outstanding  leg  is  5  inches  wide; 
( b )  the  number  of  rivets  required  to  connect  the  stiffeners  to  the  web,  if 
•§--inch  rivets  are  used. 

Solution.  —  (a)  In  Art.  29  of  B.  S. ,  the  allowable  intensity  of 
bearing  on  the  ends  of  stiffeners  is  given  as  18,000  lb.  per  sq.  in. 
Then,  since  R  =  230,000,  n  =  8,  and  b  —  5,  we  have,  applying  the 
formula  in  Art.  28, 

*  "  8X  18,000  X  4.5  =  -355’  °r’  Say’  1  m'  AnS' 

(b)  Considering  a  single  stiffener,  the  value  in  bearing  on  a 
-f-inch  angle,  as  given  in  Table  XL,  is  7,220  lb.;  and  in  single  shear, 
6,600  lb.  The  latter  is  the  smaller.  The  stress  in  one  stiffener  is 
230,000  -4-  8  =  28,750  lb.,  and  the  required  number  of  rivets  is 
28,750  4-  6,600  =  4.4. 

Taking  two  stiffeners,  it  is  necessary  to  consider  the  value  of  the 
rivet  in  double  shear  at  13,230  lb.,  in  bearing  on  two  stiffeners  at 
14,440  lb.,  and  in  bearing  on  the  combined  thickness  of  web  and  two 
reinforcing  plates  if-  in.  The  last  is  evidently  greater  than  either 
of  the  other  two  values;  the  value  in  double  shear  is  the  smallest, 
and  must  be  used.  Since  the  stress  in  two  stiffeners  is  twice  that  in 
one,  and  the  value  in  double  shear  is  twice  that  in  single  shear,  the 

number  of  rivets  will  be  the  same  as  in  the  first  case  considered,  that 

>  \ 

is,  4.4,  or,  say,  5  rivets  in  each  stiffener.  Ans. 

33.  Rocker  Bearings.— The  ends  of  spans  over  75  feet 
in  length  are  supported  on  rockers  and  supplied  at  one  end 
with  rollers,  as  explained  in  Bridge  Members  and  Details. 
When  it  is  necessary,  on  account  of  high  water,  to  keep 
the  bridge  seat  close  to  the  bottom  of  the  girders,  the 


§  75 


DESIGN  OF  PLATE  GIRDERS 


35 


arrangement  represented  in  Fig.  16  is  used.  The  outstand¬ 
ing  legs  of  the  lower  flange  angles  are  cut  away  for  a  short 
distance  at  each  end  to  allow  the  lower  flange  to  enter 
between  the  vertical  plates  of  a  pedestal.  The  web  of  the 


girder  is  reinforced  at  the  end,  and  a  pin  is  passed  through 
the  pedestal  and  web;  the  pin  should  never  be  less  than 
6  inches  in  diameter.  The  design  of  the  pin,  pin  plates,  and 
pedestal  is  made  by  the  same  general  principles  that  apply 
to  pin-connected  trusses,  as  explained  in  another  Section. 


EXAMPLES  FOR  PRACTICE 

1.  If  the  maximum  reaction  at  the  end  of  the  plate  girder  repre¬ 

sented  in  Fig.  13  is  157,000  pounds,  stiffeners  5  in.  X  3-J  in.,  and 
allowable  intensity  of  bearing  18,000  pounds  per  square  inch,  what  is 
the  required  thickness  of  the  stiffener  angles?  Ans.  \  in. 

2.  If  in  example  1  the  value  of  a  rivet  in  single  shear  is  6,600 
pounds,  and  in  bearing  on  the  web  15,000  pounds,  Jiow  many  rivets 
must  be  used  in  each  stiffener  to  transmit  the  stress  to  the  web? 

Ans.  6  rivets 

3.  If  the  maximum  reaction  at  the  end  of  the  plate  girder  repre¬ 

sented  in  Fig.  15  is  275,000  pounds,  stiffeners  5  in.  X  3-g-  in.,  and 
allowable  intensity  of  bearing  18,000  pounds  per  square  inch,  what  is 
the  required  thickness  of  the  stiffener  angles?  Ans.  -p6-  in. 


DESIGN  OF  PLATE  GIRDERS 

(PART  2) 


DESIGN  OF  AN  I-BEAM  HIGHWAY 

BRIDGE 

1.  Introduction. — In  this  and  in  the  following-  Sections 
will  be  given  complete  designs  of  several  classes  and  types  of 
bridges.  The  designs  will  be  made  according  to  the  rules 
given  in  Bridge  Specifications  (a  title  that,  for  convenience, 
will  be  abbreviated  to  B.  S.).  These  examples  will  famil¬ 
iarize  the  student  with  the  principles  involved  and  the 
methods  used,  which  he  can  without  any  difficulty  extend  to 
forms  and  conditions  not  specifically  covered  in  the  present 
instruction. 

2.  Data. — As  a  first  example,  an  I-beam  highway  bridge 
will  be  designed  from  the  data  given  in  the  data  sheet  on 
page  4.  The  words  in  Italics  are  supposed  to  have  been 
written  to  fill  out  the  general  form,  which  contains  only  the 
words  printed  in  Roman  type  (see  B.  S.,  Art.  226). 

3.  Determination  of  Span. — It  is  first  necessary  to 
determine  the  location  of  the  abutments.  According  to  B.  S., 
Art.  18,  no  part  of  a  bridge  should  be  less  than  7  feet  from 
the  center  line  of  the  nearest  track,  nor  less  than  22  feet 
above  the  base  of  the  rail.  This  condition  applies  also  to 
abutments  and  underneath  clearance  lines  for  overhead 
bridges.  As  the  faces  of  abutments  are  usually  rough  and 
extend  somewhat  beyond  the  neat  lines,  it  is  well  to  locate 
the  neat  lines  at  the  base  of  the  rail  7  feet  6  inches  from  the 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

§70  * 


2 


DESIGN  OF  PLATE  GIRDERS 


§76 


center  line  of  the  track,  making  them  (as  there  are  two 
tracks  13  feet  center  to  center)  7  feet  6  jnches  -f-  13  feet 
-f  7  feet  6  inches  =  28  feet  apart.  The  faces  of  abutments 
are  sometimes  made  plumb  (vertical),  in  order  to  shorten 


the  span,  and  sometimes  battered,  according  to  the  judg¬ 
ment  of  the  engineer.  In  the  present  case,  allowance  will 
be  made  for  a  batter  of  i  inch  per  foot  in  each  abutment: 
then,  the  distance  between  the  faces  will  increase  at  the  rate 


76 


DESIGN  OF  PLATE  GIRDERS 


3 


of  i  +  2  =  1  inch  for  every  foot  above  the  base  of  the  rail, 
as  far  as  the  bottom  of  the  bridge  seat  or  coping.  Bridge 
seat  stones  are  usually  made  from  12  inches  thick  for  short 
spans  to  24  inches,  and  in  some  cases  more,  for  long  spans. 
In  the  present  case,  a  thickness  of  16  inches  will  be  sufficient. 
Allowing  1  inch  for  the  thickness  of  the  sole  plate  and  1  inch 
for  the  bedplate  makes  the  distance  from  the  underneath 
clearance  line  (the  bottom  of  the  I  beam)  to  the  bottom  of 
the  bridge  seat  16  +  1  +  1  =  18  inches,  and  the  distance 
from  the  base  of  the  rail  to  the  bottom  of  the  bridge  seat 
22  feet  —  1  foot  6  inches  =  20  feet  6  inches.  Then,  as  the 
distance  between  the  abutments  increases  1  inch  for  each 
foot,  it  will  increase  20i  inches,  or  1  foot  8i  inches,  in 
20  feet  6  inches,  and  the  distance  between  the  neat  lines 
under  the  bridge  seat  will  be  28  feet  +  1  foot  8i  inches 
=  29  feet  8i  inches,  as  represented  in  Fig.  1,  which  is  the 
bridge- seat  plan,  that  is,,  the  drawing  of  the  bridge  seat. 
[It  will  be  noticed  that  here  the  word  plan  is  used  in  the 
sense  of  drawing  or  drawings ,  not  in  the  sense  of  a  top 
view.  In  reality,  the  drawings  in  Fig.  1  show  both  a  top 
view  (a)  and  a  cross-section  (£).] 

4.  For  a  span  of  this  length,  the  edge  of  the  bedplate 
should  not  come  closer  than  3  or  4  inches  to  the  neat  line, 
and  should  not  be  set  much  farther  back  than  this,  as  it 
lengthens  the  span.  In  the  present  case,  it  will  be  set 
4f  inches  back  at  each  abutment,  making  the  clear  distance 
between  bedplates  29  feet  8i  inches  +  4f  inches  +  4|  inches 
=  30  feet  6  inches.  Bedplates  are  seldom  made  less  than 
12  inches  in  length;  this  is  long  enough  for  this  span,  and 
makes  the  total  length  of  I  beams  30  feet  6  inches  +  1  foot 
+  1  foot  =  32  feet  6  inches,  and  the  distance  center  to 
center  of  bedplates  (the  span)  31  feet  6  inches^  or  378  inches. 
The  parapets  are  usually  set  3  inches  from  the  ends  of  the 
beams;  that  makes  them,  in  this  case,  33  feet  apart. 

5.  Deptli  and  Spacing  of  Beams. — As  this  span  is  less 

than  35  feet,  rolled  beams  will  be  used.  According  to  B.  S ., 
Art.  92,  they  cannot  be  less  than  378  30  —  12.6  inches  in 


4 


DESIGN  OF  ELATE  GIRDERS 


GENERAL  DATA 

For  bridge  over  Delaware^  Lackawa?ina,  &  Western  Railroad 
aj.  _ Elmhurst ,  Pennsylva7iia _ _ 

Length  and  general  dimensions _ T°  sPan  ^wo  tracks  33jeet  _ 

center  to  center  _ _ _ 

Skew  or  angle  of  abutments  with  center  line  of  bridge 

Width  of  bridge  and  location  of  trusses-—-/^  cJeaT.. 

No  trusses _ _ _ 

Floor  system  ®ne  ^ayer  °f  3-inch  oak  plank- on  nailing  pieces 

and  steel  beams 

Number  and  location  of  tracks _ W<7  irac^s _ _ 

Loadin'*'  Art.  US  (-5)  Bridge  Specificatio?is 

Description  of  abutments  Cement-concrete  abutments _ 

Distance  from  floor  to  clearance  line _ Not  more  than  3  feet 

high  water _ 


« < 


u 


i  < 


u 


( « 


( l 


<1 


14 


low  water _ 

river  bottom. 

I 

Character  of  river  bottom- _ 

Usual  season  for  floods _ 


Name  of  nearest  railroad  station  Elmhurst,  Pe?insylvama, 
D L .  and  W.  R.  R. 

2  miles 


Distance  to  nearest  railroad  station _ _ 

Time  limit _ months  from  date  of  award  of  ccmtract 


Ndme  of  Engineer 


International  Textbook  Company 


Address  of  Engineer 


Scranton ,  Pemisylvania 


Remarks  i‘ave  a  tight  board  fence  at  each  side  at  least  5  feet 
6  inches  above  the  top  of  the  floor 


§76 


DESIGN  OF  PLATE  GIRDERS 


5 


depth.  Table  XIV*  shows  that  the  next  depth  of  beam  is 
15  inches.  In  finding  the  spacing  of  beams,  it  is  first  neces¬ 
sary  to  determine  the  distance  between  the  outside  beams. 
In  the  present  case,  a  roadway  of  20  feet  between  wheel- 
guards  is  required;  the  fence  will  be  placed  6  inches  outside 
of  the  inner  edges  of  the  wheel-guards;  then,  the  clear  dis¬ 
tance  between  the  fences  will  be  21  feet. 
A  tight  board  fence  is  specified  to  prevent 
injury  to  the  traffic  from  cinders  and 
sparks  from  the  locomotives  that  will  pass 
underneath. 

Fig.  2  shows  the  cross-section  of  a  good 
Style  of  fence  and  connection  to  the  beams; 
the  posts  are  placed  5  or  6  feet  apart.  The 
outside  beam  is  usually  a  channel,  prefer¬ 


VT 


_ .» T 
1 


-2/-5  Between  out&'cte  Cftanne/s 


Fig.  2 


ably  of  the  same  depth  as  the  I  beams.  To  assist  in  keeping 
the  fence  in  place  and  preventing  it  from  being  blown  over, 
the  channel  may  be  connected  to  the  next  beam,  at  intervals  of 
about  10  feet,  by  means  of  the  diaphragm  shown  in  Fig.  2. 


*A11  tables  referred  to  in  this  Section  are  found  in  Bridge  Tables , 
unless  otherwise  stated. 


6 


DESIGN  OF  PLATE  GIRDERS 


§76 


This  may  be  made  of  the  lightest  material  allowed — in  this 
case,  as  the  bridge  is  over  a  railroad,  f  inch  thick  ( B .  S ., 
Art.  112).  With  the  arrangement  represented  in  Fig.  2, 
the  face  of  the  channel  is  8i  inches  outside  of  the  edge  of 
the  wheel-guard,  making  the  channels  20  feet  +  82  inches 
+  82-  inches  —  21  feet  5  inches  from  face  to  face.  As  there 
will  be  one  layer  of  floor  planks  3  inches  thick,  the  beams 
cannot  be  more  than  3  feet  center  to  center  ( B .  S .,  Art.  123) . 
Five  spaces  at  3  feet  makes  15  feet,  leaving  21  feet  5  inches 
—  15  feet  =  6  feet  5  inches,  to  be  made  up  in  the  sides  of  the 
bridge.  This  requires  the  face  of  each  channel  to  be  placed 
one-half  of  6  feet  5  inches,  or  3  feet  2i  inches,  from  the  center 
of  the  first  beam;  if  a  spiking  piece  4  inches  wide  is  used  on 
the  channel,  its  center  will  be  just  3  feet  from  the  center  of  the 
next  beam.  This  spacing  of  beams  will  satisfy  all  conditions. 

6.  Live  Load. — According  to  B.  S .,  Arts.  98  (3)  and 
110,  the  live  load  should  be  either  80  pounds  per  square 
foot  or  a  steam  road  roller  acting  on  each  beam  as  two 
concentrated  loads  of  5,000  pounds,  11  feet  apart.  For 
the  former,  as  the  beams  are  3  feet  apart,  the  load  per 
linear  foot  is  3  X  80  =  240  pounds.  The  maximum  bending 
moment  occurs  at  the  center,  and,  as  the  span  is  31.5  feet,  is 

240  X  3L5  X  3L5  =  29,770  foot-pounds 

The  maximum  bending  moment  due  to  the  two  concentrated 
loads  occurs  under  one  of  the  loads  when  that  load  and  the 
center  of  gravity  of  the  two  loads  are  equidistant  from  the 
center  of  the  beam,  and,  as  explained  in  Stresses  i?i  Bridge 

Trusses ,  Part  4,  is  equal  to  AQiPPQ  ^  X  13  _  53  f00|-_ 

31.5 

pounds  at  2.75  feet  from  the  center  of  the  span.  As  the 
bending  moment  due  to  the  road  roller  is  the  greater,  it  is 
unnecessary  to  further  consider  that  due  to  the  uniform  load. 
The  shear  will  not  be  considered  in  this  example,  as  it  has 
been  found  in  practice  that,  in  all  ordinary  cases  in  bridge 
work,  an  I  beam  or  channel  that  is  strong  enough  to  resist 
the  bending  moment  is  also  strong  enough  to  resist  the  shear. 


§76 


DESIGN  OF  PLATE  GIRDERS 


7 


The  bending  moment  on  the  channel  may  be  taken  equal  to 
one-half  that  on  the  I  beams,  or  53,650  -f  2  =  26,820  foot¬ 
pounds,  as  the  load  on  the  channel  is  practically  one-half  the 
load  on  the  beam. 

7.  Dead  Load. — As  4.5  pounds  per  board  foot,  the 
weight  stated  in  B.  S.,  Art.  97,  is  rather  high  for  the  timber 
used  in  bridge  floors,  we  shall  assume  it  to  include  the 
weight  of  the  spikes  that  hold  the  floor  down,  and  the  bolts 
that  hold  the  spiking  pieces  to  the  beams.  As  the  floor 
plank  is  3  inches  thick,  its  weight  is  3  X  4.5  =  13.5  pounds 
per  square  foot,  or,  since  the  beams  are  3  feet  apart, 
3  X  13.5  —  40.5  poiind  per  linear  foot  of  beam.  The 
floor  plank  will  be  fastened  down  by  spiking  it  to  wooden 
nailing  pieces  2  to  6  inches  thick  that  are  bolted  to  the  tops 
of  the  I  beams  (see  B.  S.,  Art.  122).  In  order  to  prevent 
water  from  standing  on  the  floor,  as  it  would  do  if  the  floor 
were  level,  it  is  customary  to  make  the  floor  a  little  higher 
at  the  center  of  the  span  than  at  the  ends;  this  is  done  by 
varying  the  depth  of  the  nailing  pieces.  In  the  present  case, 
the  nailing  pieces  will  be  made  2  inches  deep  at  the  ends  of 
the  span  and  4  inches  deep  at  the  center.  As  the  top  of  the 
nailing  piece  will  be  curved,  its  average  depth  will  be  about 
3i  inches.  Its  width  should  be  at  least  equal  to  the  flange 
of  the  beam;  it  will  be  assumed  that  6  inches  is  sufficient. 
The  average  cross-section  is  then  3i  in.  X  6  in.,  equivalent 
to  If  board  feet;  this  makes  the  weight  per  linear  foot 
1.75  X  4.5  =  7.9  pounds.  The  total  weight  of  timber  sup¬ 
ported  by  each  beam  is,  then,  very  nearly  40.5  -f  7.9  =  48.4 
pounds  per  linear  foot.  As  the  maximum  bending  moment 
due  to  the  live  load  occurs  2.75  feet  from  the  center,  or  13 
feet  from  the  end  of  the  span,  it  is  necessary  to  find  the 
dead-load  bending  moment  at  that  point.  For  the  floor 
plank  and  nailing  pieces,  it  is 

43.4  X  31.5  x  13  _  (48 A  x  13)  x  jj.  =  5,820  foot-pounds 

A 

for  each  beam,  and  approximately  one-half  of  this,  or 
2,910  foot-pounds,  for  each  channel. 


8 


DESIGN  OF  PLATE  GIRDERS 


70 


8.  There  is  still  to  be  considered  the  bending  moment 
due  to  the  weight  of  the  diaphragms  represented  in  Fig.  2. 
The  distance  from  the  center  of  the  I  beam  to  the  back  of 
the  channel  is  3  feet  2j  inches;  the  diaphragm  will  be  about 
3  feet  If  inches  long,  and,  if  15-inch  beams  are  used,  about 
12  inches  deep.  Then,  as  the  weight  of  a  12"  X  t "  plate  is 
15.3  pounds  per  linear  foot,  the  weight  of  3  feet  If  inches 
is  15.3  X  3.125  —  47.8  pounds.  The  total  length  of  angle 
is  3  feet  Li  inches  +  3  feet  li  inches  -f  12  inches  +  12  inches 
=  8  feet  3  inches,  or  8.25  feet.  As  the  weight  of  a  2i"  X  2i// 
X  i"  angle  is  5.9  pounds  per  linear  foot,  the  total  weight  of 
angles  is  5.9  X  8.25  =  48.7  pounds.  In  Fig.  2,  it  may  be  seen 
that  there  are  thirty  f-inch*  rivets  in  one  diaphragm,  and  the 


weight  of  their  heads  must  be  found.  Table  XXI  gives 
8.5  pounds  for  the  weight  of  one  hundred  rivet  heads  for 
f-inch  rivets;  then,  the  weight  of  sixty  rivet  heads  will  be 
iifo  X  8.5  =  5.10  pounds.  The  weight  of  one  diaphragm  is, 
therefore,  47.8  +  48.7  +  5.1  =  101.6  pounds.  Using  four 
of  these  placed  symmetrically  on  the  span  at  distances  of 
about  10  feet,  as  shown  in  Fig.  3,  the  bending  moment  on 
the  I  beam  and  on  the  channel  due  to  them  is,  since  half  of 
each  goes  to  one  beam, 

101.6  X  10.75  -  —  -  X  10  =  580  foot-pounds 

Zi 

The  bending  moments  due  to  the  weight  of  the  beams  and 
channels  cannot  be  found  until  their  weights  are  known.  It 
is  well  to  assume  some  value,  however,  and,  if  necessary, 


DESIGN  OF  PLATE  GIRDERS 


9 


§  7(5 

correct  it  later.  An  experienced  designer  will  come  very 
close  the  first  time.  It  has  been  shown  that  the  depth 
cannot  be  less  than  15  inches;  we  shall  use  the  weight  of 
the  lightest  15-inch  beam  and  channel,  42  and  33  pounds  per 
linear  foot,  respectively,  as  given  in  Tables  XIII  and  XIV. 
For  the  I  beams,  the  bending  moment  at  the  point  of  maxi¬ 
mum  moment,  2.75  feet  from  the  center,  is 

X  13  —  (42  X  13)  X  V  —  5,050  foot-pounds 
And  for  the  channel, 

33  X  3U>  x  13  _  (33  x  13)  x  Jji  =  3;970  foot-pounds 

A 

The  guard  timber  and  fence  will  be  found  to  weigh  very 
nearly  45  pounds  per  linear  foot,  and,  as  this  weight  is 
almost  all  carried  by  the  channel,  the  moment  on  the  channel 
due  to  it  is 

—  ^  ^ X  13  —  45  X  13  X  x£~  —  5,410  foot-pounds 

A 

The  total  maximum  bending  moment  on  an  I  beam  is, 
then,  53,650  +  5,820  +  580  +  5,050  =  65,100  foot-pounds,  or 
781,200  inch-pounds. 

The  total  maximum  bending  moment  on  a  channel  is 
26,820  +  2,910  +  580  +  3,970  +  5,410  =  39,690  foot-pounds, 
or  476,300  inch-pounds.' 

9.  Allowable  Working  Stress. — The  allowable  inten¬ 
sity  of  stress  given  in  B.  S.,  Art.  103, -for  the  compression 

flange  is  20,000  —  200  X  — .  It  is  not  considered  good  prac- 

w 

tice  to  assume  that  a  wooden  floor  gives  lateral  support 
to  the  top  flanges  of  the  I  beams;  so,  if  no  bracing  is 
placed  between  the  beams,  the  unsupported  length  will  be 
31.5  X  12  =  378  inches.  Suppose  that  a  15-inch  beam  were 
used,  then,  as  the  flange  is  about  5.5  inches  wide,  the  ratio 
l  378 

—  would  be  =  68.7,  and  the  allowable  intensity  of  stress 
w  5.o 

would  be  20,000  —  200  X  68.7  =  6,260  pounds  per  square 
inch.  If,  however,  small  struts  are  placed  between  the 
beams  near  the  top  flanges,  in  the  same  relative  positions 

135—9 


•10 


DESIGN  OF  PLATE  GIRDERS 


70 


as  the  diaphragms  already  referred  to,  the  unsupported 
lengths  may  be  taken  as  10  feet,  or  120  inches,  and  the 
allowable  intensity  of  stress  for  the  I  beam  will  then  be 

20,000  -  200  x  —  =  15,640  pounds 

5.5 

In  general,  when  the  ratio  —  exceeds  40,  the  top  flanges 

w 

should  be  supported  laterally. 

As  the  bending  moment  is  781,200  inch-pounds,  the 
required  value  of  the  section  modulus  is  781,200  15,640 

=  49.95.  Consulting  Table  XIV,  it  is  found  that  the  lightest 
15-inch  beam — that  is,  a  15-inch  42-pound  beam — has  a  sec- 
tion  modulus  of  58.9.  This  beam,  therefore,  can  and  will 
be  used. 

« 

10.  Assuming  that  the  lightest  15-inch  channel  is  used, 
for  which  the  flange  is  3.4  inches  wide,  the  allowable  intensity 
of  stress  is 

20,000  —  200  X  ---  =  12,940  pounds  per  square  inch 

3.4 

Then,  as  the  maximum  bending  moment  is  476,300  inch- 
pounds,  the  required  value  of  the  section  modulus  is 
476,300  -  12,940  =  36.81.  Consulting  Table  XIII,  it  is  found 
that  a  15-inch  33-pound  channel  has  a  section  modulus  of  41.7, 
and  so  this  will  be  used. 

11.  The  bracing  angles  will  add  a  little  to  the  dead  load 
on  the  I  beams;  but,*  as  the  section  modulus  of  the  15-inch 
42-pound  I  beam  is  larger  than  required,  it  is  not  necessary 
to  consider  the  effect  of  those  angles. 

Note. — In  case  the  required  value  of  the  section  modulus  had  come 
out  larger  than  that  corresponding  to  the  assumed  size  of  the  beam, 
it  would  have  been  necessary  to  revise  the  design.  Suppose  that  it 
had  come  out  86.0.  Then,  if  a  15-inch  beam  were  used,  it  would  be 
necessary  to  use  a  15-inch  70-pound  beam,  for  which  the  section  modu¬ 
lus  is  88.5;  the  same  strength  could  be  had,  however,  by  using  an 
18-inch  55-pound  beam,  for  which  the  section  modulus  is  88.4,  thereby 
getting  the  same  strength  with  a  lighter  beam.  It  would  then  be 
necessary  to  recompute  the  bending  moment  and  allowable  intensity 
of  stress  for  the  18-inch  beam. 

12.  Depth  of  Floor. — The  distance  from  the  clearance 
line  and  from  the  top  of  the  bridge  seat  to  the  top  of  the 


135  §  76 


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"mo's?? 

\r 


r 


£0  Frames  Mark  F* 

(9) 


FZfxZfrfx8§'L,$' 


r  &. 

R/t/e/s  -g  /n  d/ame/er 
s  ¥ 

Bo/fs-g  m  d/amefer 


(d) 


'  • 


1  :  ' 


' 


'  ■ 

UU4&  .W 


§76 


DESIGN  OF  PLATE  GIRDERS 


11 


floor  can  now  be  found.  The  vertical  distances  at  the  center 
of  the  span  are  3  inches  of  plank,  4  inches  of  nailing  strip, 
and  15  inches  for  the  I  beams  and  channels,  making  22  inches 
for  the  depth  of  floor  at  the  center,  as  represented  in 
Fig.  1  ( b ).  In  Art.  3,  2  inches  was  allowed  for  sole  plates 
and  bedplates  under  the  beams;  the  bridge  seat  is,  therefore, 
24  inches  below  the  floor  at  the  center  of  the  span,  and,  since 
the  nailing  pieces  are  2  inches  deep  at  the  ends,  the  bridge 
seat  is  22  inches  below  the  floor  at  the  ends.  If  the  tops  of 
the  parapets  a,  a,  Fig.  1  (b) ,  are  made  level  with  the  floor, 
they  must  be  22  inches  high. 

13.  General  Plan  or  Detail  Drawings. — Fig.  4  is  a 
detail  drawing  of  the  bridge  that  has  just  been  designed, 
and  gives  all  the  information  necessary  for  its  manufacture. 
It  is  customary,  in  drawing  the  plan  and  elevation,  to 
show  a  portion  of  the  floor  and  fence  in  its  finished  condi¬ 
tion,  as  at  ( a )  and  (b) ,  and  the  remainder  with  the  floor  and 
fence  removed,  as  at  ( c )  and  {d) .  One  end  of  a  channel 
and  several  beams  are  usually  shown  with  the  top  flange  cut 
away,  in  order  to  show  the  detail  of  the  connection  of  the 
beams  to  the  sole  plates.  The  diaphragms,  sometimes  called 
frames,  are  marked  A,,  and  the  cross-struts,  which  also  are 
called  frames,  are  marked  F*.  Frames  of  both  kinds  are 
shown  to  a  larger  scale  at  (/)  and  (g) . 

The  holes  for  the  anchor  bolts  at  one  end  are  made  circu¬ 
lar  and  i  inch  larger  in  diameter  than  the  bolts;  at  the  other 
end,  they  are  made  li  inches  wide  and  If  inches  long, 
allowing  f  inch  for  expansion  and  contraction. 

In  a  bridge  of  this  size,  the  diaphragms  or  frames  are 
sometimes  bolted  instead  of  riveted  to  the  beams,  to  avoid 
the  expense  of  setting  up  a  riveting  plant  for  so  small  a 
number  of  rivets. 


12 


DESIGN  OF  PLATE  GIRDERS 


S  76 


DESIGN  OF  AN  I-BEAM  RAILROAD 

BRIDGE 


14.  Data. — An  I-beam  railroad  bridge  will  now  be 
designed  from  the  data  given  on  page  13. 


15.  Determination  of  Span. — The  distance  between 
neat  lines  under  bridge  seats  is  20  feet.  If  the  bearing 


DESIGN  OF  PLATE  GIRDERS 


S  70 


o 

o 


For  bridge  over 
at _ _ 


GENERAL  DATA 

French  Creek 


Redlands ,  California 


Length  and  general  dimensions _ 20  feet  between  ncal  lines 

under  bridge  seats  ' _ _ 


Skew  or  angle  of  abutments  with  center  line  of  bridge_J?^_ 
Width  of  bridge  and  location  of  trusses^ _ No_trusses_ _ 


Floor  system  Standard  tie-floor  on  steel  stringers  or  I  beams 
Number  and  location  of  tracks  %  tracks  lo  feet  center  to  center 
Loading  Cooper's  E50 ,  as  represented  in  Bridge  Specifications , 

Art.  24  _ 

T  r\(-  oVMiftvmnlc  C C  III  Cll  t  COllC  1C  t C 


Distance  from  floor  to  clearance  line 

Not  greater  than 

distance  to  high  water 

Distance  from  floor  to  high  water  - 

8  feet 

t»  «<  <<  (<  , 

low  water 

13  feet 

<►  <<  ((  (C  . 

river  bottom 

15  feet 

Character  of  river  bottom  2  feet  gravel,  3  Let  shale,  then  solid 

rock  20  feet  below  base  of  rail 

Usual  season  for  floods  April  and  May 

Name  of  nearest  railroad  station 

Redlands,  California 

Distance  to  nearest  railroad  station. 

5  miles 

Time  limit¬ 


ed  days 


Name  of  Engineer _ _ _ _ 

Address  Berkeley,  California 

Remarks _ 


Henry  Jones 


14 


DESIGN  OF  PLATE  GIRDERS 


76 


plates  are  made  12  inches  wide,  and  set  so  that  their  edges 
are  6  inches  back  of  the  neat  line,  the  total  length  of  the 
beams  will  be  20  feet  +  1  foot  6  inches  4-  1  foot  6  inches 
=  23  feet;  and  the  distance  center  to  center  of  bearings  (the 
span),  1  foot  less,  or  22  feet.  If  3  inches  is  left  at  each  end, 
the  parapets  will  be  23  feet  6  inches  apart.  The  bridge 
seats  will  be  made  1  foot  6  inches  thick.  The  bridge-seat 
plan  is  represented  in  Fig.  5.  The  distance  from  the  base 
of  the  rail  to  the  top  of  the  bridge  seat  cannot  be  found 
until  after  the  bridge  is  designed.  The  top  of  the  parapet  is 
made  7i  inches  below  the  base  of  the  rail. 

16.  Depth  and  Spacing  of  Beams. — The  depth  and 
the  spacing  of  beams  depend  on  the  maximum  bending 
moment  and  required  value  of  the  section  modulus.  It  is 
considered  better  practice  to  place  two  beams  under  each 
rail  than  one;  where  necessary,  three  are  used.  The  beams 
under  each  rail  are  bolted  together  and  made  to  act  as  one 
by  means  of  cast-iron  separators  or  spacers,  as  illustrated 
in  Table  XV;  these  are  located  about  5  or  6  feet  apart 
along  the  beams,  but  are  not  to  be  assumed  as  support¬ 
ing  the  top  flanges  laterally.  Lateral  support  is  furnished 
by  lateral  bracing  so  arranged  that  the  ratio  of  unsupported 
length  to  width  of  flange  shall  not  exceed  12  (see  B.  S ., 
Art.  87). 

17.  Live  Load. — The  live  load  is  represented  in  Fig.  3 
of  B.  S .  By  applying  the  conditions  for  maximum  moment, 
it  is  found  that  it  occurs  when  there  are  four  driving  axles 
on  the  span,  under  the  second  (or  third)  driver  when  that 
driver  is  1.25  feet  from  the  center  of  the  span,  and  is  equal  to 

4  X  50,000  X  9-75  X  9.75  _  50j000  x  5  =  614,200  foot-pounds. 

A  A  « 

18.  Impact  and  Vibration. — The  formula  for  impact 

and  vibration  is  1  =  -  X  S  (B.  S.,  Art.  25).  In  this 

A  T  ouu 

case,  as  the  moment  is  required,  the  value  of  the  moment 
found  in  the  last  article  should  be  substituted  for  S;  and,  as 


§76 


DESIGN  OF  PLATE  GIRDERS 


15 


the  entire  span  must  be  loaded  in  order  to  produce  the 
maximum  moment,  L  —  22.  Therefore, 


/  = 


X  614,200  —  572,200  foot-pounds 

22  +  300 


19.  Dead  Load. — The  weight  w  per  linear  foot  of 
I-beam  bridges  of  this  class  is  given  very  closely  by  the 
formula  w  =  25  /  ( B .  S.,  Art.  242).  In  this  case,  /  =  22, 
and,  therefore,  w  —  25  X  22  —  550  pounds  per  linear  foot. 
The  weight  of  track  can  be  taken  as  400  pounds  per  linear 
foot  ( B .  S.y  Art.  23).  The  maximum  live-load  moment 
occurs  very  near  the  center  of  the  span,  and  it  will  be  suffi¬ 
ciently  accurate  to  find  the  dead-load  moment  at  the  center, 
which  is 


(550  +  400)  X  22  X  22 
8 


57,500  foot-pounds 


20.  Wind  Load. — It  is  unnecessary  to  compute  the 
stresses  in  the  laterals  of  I-beam  bridges.  If  the  smallest- 
sized  angle  allowed  is  used — in  this  case,  in.  X  3|  in.  X  f  in. 
— it  is  sufficiently  strong  to  resist  any  wind  stresses.  Accord¬ 
ing  to  B.  S.y  Art.  27,  the  wind  pressure  on  the  train  is 
300  pounds  per  linear  foot,  applied  7  feet  above  the  top  of 
the  rail.  Ordinarily,  the  lateral  system  will  be  about  2  feet 
below  the  top  of  the  rail,  or  about  9  feet  below  the  center  of 
wind  pressure.  Then,  as  the  beams  will  be  placed  6  feet 
6  inches  center  to  center,  the  additional  load  on  the  leeward 
beams  (as  explained  in  Stresses  in  Bridge  Trusses,  Part  5) 


will  be 


300  X  9 
6.5 


=  415  pounds  per  linear  foot,  and  the  bend¬ 


ing  moment  at  the  center  due  to  it  will  be 

415_X22X_22  =  25  l00  foot.pounds 
8 

As  this  is  so  small,  it  is  sometimes  neglected.  In  the 
present  case,  it  is  less  than  2  per  cent,  of  the  total  moment, 
but,  there  being  no  reason  why  it  should  not  be  considered, 
it  will  be  taken  into  account. 


21.  Total  Moment. — The  total  moment  is  equal  to  the 
sum  of  the  several  moments  just  found,  and  is  as  follows: 


DESIGN  OF  PLATE  GIRDERS 


16 


614,200  +  572,200  +  57,500  +  25,100  =  1,269,000  foot-pounds 
=  15,228,000  inch-pounds. 

22.  Section  Modulus. — As  it  is  required  that  the 
flanges  shall  be  supported  laterally,  the  full  value  of  16,000 
pounds  per  square  inch  can  be  used  for  the  allowable  intensity 
of  stress,  since  the  ratio  of  width  to  unsupported  length  will 
be  less  than  20  (see  B.  S.}  Art.  29).  Then,  the  required 
value  of  section  modulus  is  15,228,000  -r-  16,000  =  951.75. 

If  four  beams  are  used  (two  under  each  rail),  the  required 
value  of  the  section  modulus  for  each  will  be  951.75  -r-  4 
=  237.94.  Consulting  Table  XIV,  it  is  found  that  the 
heaviest  I  beam  made  has  a  section  modulus  of,  198.4,  which 
is  not  enough.  Therefore,  more  beams  must  be  used.  If 
six  beams  are  used  (three  under  each  rail),  the  required 
value  of  the  section  modulus  for  each  will  be  951.75  —  6 
=  158.62.  Consulting  Table  XIV,  it  is  found  that  a. 20-inch 
95-pound  I  beam  has  a  section  modulus  of  160.7,  and  a 
24-inch  80-pound  I  beam  has  a  section  modulus  of  174.  If 
it  were  necessary  to  keep  the  distance  from  the  base  of  the 
rail  to  the  underneath  clearance  line  as  small  as  possible, 
the  20-inch  beams  would  be  used.  In  the  present  case,  as 
there  are  practically  no  restrictions,  the  24-inch  beams  will 
be  used,  as  they  are  lighter  and  therefore  more  economical. 
On  account  of  their  larger  value  of  section  modulus,  the 
24-inch  beams  are  also  stronger  than  the  20-inch  beams. 


23.  Deptli  of  Bridge. — In  B.  S.,  Art.  48,  it  is  stated 
that  standard  ties  are  framed  to  7i  inches  in  depth  over 


,  :  . 

.  :  .  . 


t 


■i 

'  '■  .  ■  - 


e-e ■ 


Base  of  f?a// 


135  §76 


Fic 


! 


I 


Cross  Secf/on  on  B-. 


;  ■  *;• 


. 

. 


. 

-  .  *,  -4  v .  : 

- 


■  •'  -  ‘  - 


■ 

•** .  *  J  ■  '/■ 


■-I: 

. 

'  .  L‘  " 


v.  , 


§76 


DESIGN  OF  PLATE  GIRDERS 


17 


stringers  and  girders  6  feet  6  inches  center  to  center. 
Then,  the  distance  from  the  base  of  rail  to  the  underneath 
clearance  line,  as  represented  in  cross-section  in  Fig.  6,  is 
7h  inches  +  24  inches  =  2  feet  7i  inches.  Allowing  1  inch 
for  the  sole  plate  and  1  inch  for  the  bedplate  gives  2  feet 
9}  inches  from  the  base  of  the  rail  to  the  top  of  the  bridge 
seat,  as  represented  in  Fig.  5. 

24.  Plan.- — Fig.  7  is  a  detail  drawing  of  the  bridge  that 
has  just  been  designed,  and  shows  the  customary  method  of 
arranging  the  lateral  system.  The  lateral  angles  are  con¬ 
nected  to  plates  that  are  riveted  to  angles  attached  to  the 
inside  beams.  The  lateral  truss  is  placed  as  high  as  is  pos¬ 
sible  without  interfering  with  the  top  flanges  of  the  beams. 
The  two  sets  of  I  beams  are  connected  near  the  ends  by 
diaphragms  or  frames,  and  at  the  panel  points  of  the  lateral 
truss  by  means  of  single  angles.  It  is  customary  to  show 
the  top  view  of  the  I  beams,  and  to  consider  a  portion  of  the 
top  flange  removed  at  each  lateral  connection  and  at  the  end 
of  one  set  of  beams,  in  order  to  show  more  clearly  the  detail 
of  the  connection  of  the  laterals  to  the  beam  and  of  the  sole 
plates  to  the  lower  flanges. 

For  I-beam  bridges  longer  than  about  18  feet,  three  panels 
are  used  in  the  lateral  systems;  for  shorter  bridges,  two 
panels  are  employed.  The  panels  are  usually  made  equal. 
In  locating  the  rivets  in  the  lateral  connection  plates,  great 
care  must  be  taken  that  the  different  angles  connecting  to 
the  plate  do  not  interfere  with  one  another.  It  is  well  to  lay 
out  each  connection  plate  on  a  large  sheet  full  or  half  size 
and  draw  each  angle  in  its  proper  position,  leaving  about 
i  inch  clearance  between  the  different  angles  that  come  close 
together. 

The  process  of  laying  out  the  lateral  system  is  frequently 
perplexing  to  a  beginner,  but  is  very  simple  after  a  little 
experience  has  been  had.  The  different  steps  will  be  briefly 
outlined.  The  end  frames  are  first  located  near  the  ends 
in  such  a  position  that  they  will  not  interfere  with  the  anchor 
bolts  nor  with  the  rivets  that  connect  the  sole  plates  to  the 


18 


DESIGN  OF  PLATE  GIRDERS 


§76 


beams.  This  can  be  done  by  locating  the  frames  about 

1  inch  from  the  sole  plates.  In  Fig.  7,  the  backs  of  the 
angles  that  serve  as  flanges  for  the  frames  are  1  foot  1  inch 
from  the  ends  of  the  I  beams.  These  angles  are  3i  inches 
wide,  and,  according  to  Table  XII,  the  gauge  lines  are 

2  inches  from  the  back  edges.  This  makes  the  gauge  lines 
of  the  end  frames  1  foot  3  inches  from  the  ends  of  the  span 
and  23  feet  —  1  foot  3  inches  —  1  foot  3  inches  —  20  feet 
6  inches  from  each  other.  This  distance  is  divided  into 
three  equal  spaces  of  6  feet  10  inches  each,  thus  locating 
the  gauge  lines  of  the  angles  that  act  as  struts  between  the 
beams  at  the  intermediate  points. 

The  three  beams  that  form  each  side  of  the  bridge  are 
bolted  together  with  their  centers  7f  inches  apart,  as  given 
in  Table  XV,  and  each  set  of  three  is  placed  with  its  center 
6  feet  6  inches  from  that  of  the  other.  This  makes  the  inside 
beams  6  feet  6  inches  —  7f  inches  —  7|  inches  =  5  feet 
2i  inches  apart.  Since  the  webs  of  these  beams  are  i  inch 
in  thickness  (Table  XIV),  the  clear  distance  between  them  is 
5  feet  2  inches.  The  lug  or  hitch  angles  that  are  used  to 

connect  the  plates  to  the  webs  of  the  inside  I  beams  are 

3i  inches  wide,  with  the  gauge  lines  2  inches  from  the  webs. 
This  makes  these  gauge  lines  5  feet  2  inches  —  2  inches 
—  2  inches  =  4  feet  10  inches  apart.  The  gauge  lines  of 
these  hitch  angles  and  those  of  the  cross-frames  or  struts, 
located  in  the  preceding  paragraph,  are  commonly  called 
working  lines  for  the  lateral  trusses.  They  can  be 

considered  as  the  center  lines  of  the  chords  and  the 
panel  points,  respectively.  The  diagonal  lines  connecting 
the  intersections  of  these  gauge  lines  locate  the  diagonals 
of  the  lateral  truss.  In  Fig.  7,  they  are  taken  as  the 

gauge  lines  of  the  laterals.  In  some  cases,  the  center  of 
gravity  of  the  angle  is  made  to  coincide  with  the  diagonal 
between  the  working  lines;  in  a  bridge  as  small  as  that 
now  under  consideration,  it  matters  little  which  method  is 
used. 

The  next  step  is  to  find  the  length  of  the  diagonal.  Each 
of  these  lines,  together  with  the  working  lines,  forms  a  right 


76 


DESIGN  OF  PLATE  GIRDERS 


19 


triangle  whose  two  legs  are  6  feet  10  inches  and  4  feet 
10  inches,  respectively.  Then,  the  length  of  the  diagonal  is 

V(6'10")’  -M4'10");  =  8  feet  4*  inches 

The  rivets  at  the  ends  of  the  laterals  are  next  located  by 
laying  out  the  connection  plates  full  or  half  size,  as  previously 
described. 

In  detailing  bridge  work,  it  is  frequently  necessary  to  find  the 
length  of  the  hypotenuse  of  a  right  triangle  when  the  legs, 
commonly  called  the  coordinates  in  this  work,  are  known. 
The  principle  for  finding  the  hypotenuse  is  simple,  but  the 
arithmetical  work  is  laborious,  especially  when  the  coordinates 
are  given  to  small  fractions,  such  as  sixteenths  of  an  inch. 
To  shorten  this  work,  tables  are  commonly  employed.  There 
are  several  books  on  the  market  that  contain  tables  giving 
the  squares  of  distances  that  occur  in  feet,  inches,  and  frac¬ 
tions  of  an  inch.  In  using  such  tables,  the  squares  of  the 
coordinates  are  copied  and  added;  the  length  corresponding 
to  the  square  root  of  the  sum  is  then  taken  directly  from  the 
table. 


DESIGN  OF  A  PLATE-GIRDER 
RAILROAD  BRIDGE 

25.  Data. — As  the  next  example  of  practical  design  will 
be  taken  a  deck  plate-girder  railroad  bridge,  the  data  sheet 
for  the  construction  of  which  is  given  on  page  20. 

26.  Determination  of  Span. — It  is  first  necessary  to 
determine  the  location  of  the  abutments.  It  is  required  that 
the  clear  distance  between  them  at  the  level  of  the  curb  be 
made  50  feet.  There  is  one  electric-car  track  in  the  center 
of  tfte  street,  and  it  may  be  assumed  that  the  top  of  the  rail 
is  level  with  the  top  of  the  curb.  According  to  B.  S., 
Art.  94,  the  lowest  line  of  overhead  bracing  in  through 
bridges  for  street  railways  shall  not  be  lower  than  15  feet 
from  the  top  of  the  rail.  This  condition  applies  equally 
well  to  the  underneath  clearance  of  bridges  over  street- 
railroad  tracks.  In  the  present  case,  the  underneath  clear¬ 
ance  line  of  the  bridge  will  be  placed  15  feet  above  the  top 


GENERAL.  DATA 


For  bridge  over _ _ Sumner  Street _ 

Cincinnati i  Ohio 

Length  and  general  dimensions  ®ne  sPan  0V€r'  street  50  feet 
wide  at  the  level  of  the  curb ,  with  one  electric-car  track  at  the 
coiter 

Skew  or  angle  of  abutments  with  center  line  of  bridge—?.— _ 

Width  of  bridge  and  location  of  trusses  ho  trusses. _ Space__ 

deck  girders  according  to  Bridge  Specifications ,  Art.  16  __ 

Floor  system  Standard-tie  floor.  See  Bridge 

Specifications ,  Art.  48 _ -- _  -t: 

Number  and  location  of  tracks  %  tracks  lb  feet  center  to  center 
Loading  Cooper's  E50 ,  as  represented  in  Bridge 

Specifications ,  Art.  24 

Description  of  abutments _ Granite  abutments ;  front  faces 

even  with  street  lines 

Distance  from  floor  to  clearance  line  N°t  more  than  6  feet 
6  inches 


Distance  from  floor  to  high  water. 


<  < 


a  u 


No  zvater 

a  it 


( i 


i  i 


low  water _ 

river  bottom. 

Character  of  river  bottom _ 

Usual  season  for  floods _ _ _ 


i  i 


i  i 


Name  of  nearest  railroad  station 


Cincinna  ti ,  Oh  io 


Distance  to  nearest  railroad  station _ _ 

Time  limit _ .90  days 


3  miles 


Name  of  Engineer. 


Address  of  Engineer _ 

Remarks  Above-described  bridge  is  to  replace  the  bridge  at 

present  in  use.  New  abutments  will  be  built  by  the  Railroad 

Company.  Contractor  will  furnish  bridge-seat  plan  within 

10  days  from  award  of  contract 


20 


§76 


DESIGN  OF  PLATE  GIRDERS 


21 


of  the  rail,  and  the  top  of  the  bridge  seat  will  be  made  level 
with  that  line.  Bridge  seats  for  this  length  of  span  should 
be  not  less  than  18  inches  thick;  using  this  thickness,  the 
distance  from  the  top  of  the  rail  to  the  neat  line  under  the 
bridge  seat  will  be  15  feet  —  1  foot  6  inches,  or  13  feet 
6  inches.  If  the  face  of  each  abutment  is  battered  i  inch 
per  foot,  the  abutments  will  be  13i  inches  farther  apart 
under  the  bridge  seat  than  at  the  top  of  the  curb,  or,  in  this 
case,  50  feet  +  1  foot  li  inches  =  51  feet  li  inches.  Bed¬ 
plates  for  deck  plate  girders  are  usually  made  about  20  inches 
long  for  spans  of  50  feet,  and  about  24  inches  long  for  spans 
75  feet  long,  with  the  front  edge  from  6  to  9  inches  behind 
the  neat  line.  For  the  span  under  consideration,  the  plates 
will  be  made  22  inches  in  length  and  set  with  the  front  edges 
6i  inches  behind  the  neat  line.  The  center  of  the  bedplate  is 
then  11  inches  +  6i  inches  =  17t  inches,  behind  at  each  end 
of  the  span;  the  span  is  51  feet  li  inches  -f  1  foot  5|  inches 
+  1  foot  5i  inches  =  54  feet;  and  the  total  length  of  the 
girder  is  22  inches  more  than  this,  or  55  feet  10  inches. 
For  a  girder  of  this  length,  the  parapets  should  not  come 
nearer  than  4  inches  to  the  ends.  In  this  case,  they  will  be 
made  56  feet  6  inches  apart. 

27.  Depth  and  Spacing  of  Girders. — Deck  girders 
are  usually  made  about  one-ninth  or  one-tenth  of  the  span 
in  depth.  When  the  distance  from  the  base  of  the  rail  to 
the  clearance  line  is  specified,  the  depth  of  the  girder  must 
be  chosen  so  as  not  to  exceed  it.  The  depth  of  the  tie  and 
the  thickness  of  the  flange  plates  will  usually  occupy  about 
1  foot  of  the  depth.  In  the  present  case,  as  the  specified 
distance  is  6  feet  6  inches,  the  depth  of  the  girder,  or  the 
width  of  the  web,  should  not  exceed  5  feet  6  inches.  If  the 
depth  of  the  girder  is  made  one-tenth  of  the  span,  it  will  be 
54  4-  10  =  5.4  feet.  It  is  well,  when  possible,  to  use  an 
even  foot  or  half  foot  for  the  width  of  web;  in  this  case, 
5.5  feet,  or  66  inches,  will  be  used.  The  backs  of  the  flange 
angles  are  usually  placed  i  inch  farther  apart,  or,  in  this 
case,  66i  inches.  This  allows  for  slight  irregularities  in  the 


22 


DESIGN  OF  PLATE  GIRDERS 


76 


edges  of  the  web-plates,  and  prevents  the  edges  from  inter¬ 
fering  with  the  flange  plates.  As  the  span  is  less  than 
70  feet,  the  girders  will  be  6  feet  6  inches  center  to  center 
(see  B.  A.,  Art.  16). 

The  bridge-seat  plan  is  represented  in  Fig.  8.  The  dis¬ 
tance  from  the  base  of  the  rail  to  the  clearance  line  or  the 


B 


B 


Center  L/ne  of  G/rcter, , 


Center  Line  of  Track 


Center  Line  of  G/rcter 


"ck  <o 

—  %£  ' 1 — s 

_ 2_j_ 


Center  L/ne  of  G /refer 


55 


Center  L/ne  of  Tract 
Center  Line  of  Girder 


^5  'O 

JLi.. 


B 


a 


a 


bridge  seat  is  not  given,  as  this  distance  cannot  be  determined 
until  after  the  girders  have  been  designed. 

28.  Dead  Load. — The  formula  for  the  weight  per 
linear  foot  of  a  deck  plate-girder  railroad  bridge  for  the 
specifications  referred  to  in  the  data  sheet,  and  for  Cooper’s" 
E50  loading,  is  given  in  Art.  242,  B.  S .,  as 

w  —  500  +  8  l  =  500  -f  8  X  54  =  930  pounds,  nearly 
The  weight  of  the  track  will  be  taken  as  400  pounds, 
making  the  total  dead-weight  930  -f-  400  —  1,330  pounds 
per  linear  foot  for  one  track  (two  girders).  As  explained 
in  Design  of  Plate  Girders ,  Part  1,  it  is  necessary  to 


§76 


DESIGN  OF  PLATE  GIRDERS 


23 


calculate  the  moments  and  shears  at  several  points  along 
the  girder.  In  the  present  case,  they  will  be  calculated 
at  the  center  and  at  distances  of  5,  10,  15,  and  20  feet  from 
the  end  of  the  span;  besides,  the  shear  at  the  end  must  be 
computed. 

The  dead-load  moments,  in  foot-pounds,  are  as  follows: 

At  the  center, 

1,330  X  54  X  54  =  4g4  g0g 
8 


At 

At 

At 

At 


20  feet  from  the  end, 

1,330  X  54  go  _  20x20 

2  2 

15  feet  from  the  end, 

1,330  X  54  15  _  1,330  X  15  X  15 

2  2 

10  feet  from  the  end, 

1,330  X  54  10  _  1,330  X  10  X  10 

2  2 

5  feet  from  the  end, 

1,330  X  54  5  _  1,330  X  5  X  5  _ 

2  2 


=  452,200 

=  389,000 

=  292,600 

162,900 


The  dead-load  shears,  in  pounds,  are  as  follows: 


At 

the  end, 

CO 

to  ° 

X 

54 

04  -  35,910 

At 

5  feet  from  the  ei 

ad, 

35,910  ■ 

-  5 

X 

1,330  - 

29,260 

At 

10  feet  from  the  < 

snd, 

/ 

35,910  - 

-  10 

X 

1,330  - 

22,610 

At 

15  feet  from  the  < 

2nd, 

35,910  ■ 

-  15 

X 

1,330  - 

15,960 

At 

20  feet  from  the  < 

2nd, 

35,910- 

-  20 

X 

1,330  - 

9,310 

At 

the  center, 

35,910  - 

-  27 

X 

1,330  = 

0 

29 

.  Live  Load.— 

-The 

live  load 

consists 

E50,  represented  in  Fig.  3  of  B.  S.  By  applying  the  prin¬ 
ciples  explained  in  Stresses  in  Bridge  Trusses ,  Part  4,  it  is 


DESIGN  OF  PLATE  GIRDERS 


24 


rr  /  ♦ 

i  (> 


found  that  the  greatest  moment  occurs  under  the  third 
driver  of  the  second  engine,  when  that  driver  is  .127  foot 
to  the  left  of  the  center.  The  value  of  this  moment  is 
2,703,200  foot-pounds.  The  maximum  moment  at  the  cen¬ 
ter,  in  this  case,  occurs  when  the  same  driver  is  at  the 
center,  and  is  2,702,500  foot-pounds.  As  will  be  seen, 
these  two  values  are  very  nearly  equal.  In  general,  it 
may  be  stated  that  for  spans  over  50  feet  it  is  sufficiently 
accurate  to  use  in  design  the  greatest  moment  that  can  occiir 
at  the  center  of  the  span ,  neglecting  the  consideration  that 
involves  the  locatio?i  of  the  center  of  gravity  of  the  loads . 
The  maximum  live-load  moments  and  shears  are  then  as 
follows: 

At  the  center  (under  third  driver,  second  engine),  the 
live-load  moment,  in  foot-pounds,  is  2,702,500. 

At  20  feet  from  the  end  (under  third  driver,  first  engine), 
2,563,000. 

At  15  feet  from  the  end  (under  second  driver,  first  engine), 
2,247,200. 

At  10  feet  from  the  end  (under  second  driver,  second 
engine),  1,703,700. 

At  5  feot  from  the  end  (under  first  driver,  second  engine), 
976,900. 

At  the  end  (first  driver,  second  engine),  the  live-load 
shear,  in  pounds,  is  228,900. 

At  5  feet  from  the  end  (first  driver,  second  engine) ,  195,400. 

At  10  feet  from  the  end  (first  driver,  first  engine),  163,100. 

At  15  feet  from  the  end  (first  driver,  first  engine),  130,900. 

At  20  feet  from  the  end  (first  driver,  first  engine),  101,600. 

At  the  center  (first  driver,  first  engine) ,  65,200. 


30.  Impact  and  Vibration. — The  formula  for  impact 

and  vibration  is  I  =  X  A  ( B .  S.,  Art.  25).  In  the 

A  -j-  oUU 

present  case,  the  allowance  in  terms  of  the  moments  and 
shears  must  be  found.  For  the  moments,  it  is  necessary  to 
load  the  entire  span;  then,  L  =  54,  and 


/  = 


m  X  M  =  .84746  M 


§76 


DESIGN  OF  PLATE  GIRDERS 


25 


The  allowances  are: 

Location 

Center 

20  feet  from  the  end 
15*feet  from  the  end 
10  feet  from  the  end 
5  feet  from  the  end 


Moment,  in  Foot-Pounds 
.84746  X  2,702,500  =  2,290,300 
.84746  X  2,563,000  =  2,172,000 
.84746  X  2,247,200  =  1,904,400 
.84746  X  1,703,700  =  1,443,800 
.84746  X  976,900  =  827,900 


As  the  length  of  track  that  must  be  loaded  to  produce  the 
greatest  shears  is  different  for  different  sections,  the  allow¬ 
ance  for  impact  and  vibration  will  be  a  different  proportion 
of  the  maximum  shear  in  each  case.  It  has  been  found  that 
the  maximum  shear  at  each  section  occurs  when  the  first 
driver  is  at  the  section,  for  which  position  the  first  wheel  is 
8  feet  beyond  the  section.  The  length  of  loaded  track  for 
sections  within  8  feet  of  the  end  of  the  span  is,  therefore, 
54  feet;  for  other  sections  it  is  equal  to  the  distance  of  the 
section  from  the  other  end  of  the  span  plus  8  feet.  The 
proportional  allowances  are  as  follows: 

At  the  end  and  5  feet  from  the  end,  the  length  L  of  loaded 
portion  is  54;  the  proportional  allowance,  /  =  .84746  6*. 
At  10  feet  from  the  end,  L  —  52;  /  =  Mi  S  =  .8523 

At  15  feet  from  the  end,  L  =  47;  /  =Hf5  =  .8646  5 

At  20  feet  from  the  end,  L  =  42;  /  =  Iff  =  .8772  S 

At  the  center,  L  =  35;  /  ==  iHHr  S  =  .8955  6* 

The  allowances  for  shear  are,  therefore,  as  follows: 


Location 

End 

5  feet  from  the  end 
10  feet  from  the  end 
15  feet  from  the  end 
20  feet  from  the  end 
Center 


Shear,  in  Pounds 
.84746  X  228,900  =  194,000 
.84746  X  195,400  =  165,600 
.8523  X  163,100  =  139,000 
.8646  X  130,900  =  113,200 
.8772  X  101,600  =  89,100 
.8955  X  65,200  =  58,400 


31.  Wind  Pressure. — In  this  article,  we  shall  consider 
only  the  increase  in  moments  and  shears  caused  in  the  leeward 
girder  by  the  overturning  effect  of  the  wind;  this  increase  is 

P  h 

calculated  by  the  formula  w  —  — — ,  in  which  P  is  the  wind 

b 


135—10 


26 


DESIGN  OF  PLATE  GIRDERS 


§76 


pressure  per  linear  foot  of  train,  and  w  is  the  vertical  load 
per  linear  foot  of  girder,  due  to  the  wind  pressure  (see 
Stresses  in  Bridge  Trusses ,  Part  5).  The  center  of  the  wind 
pressure  is  7  feet  above  the  top  of  the  rail  (B.  S.,  Art.  27), 
and  the  top  lateral  bracing  is  generally  about  2  feet  below 
the  top  of  the  rail;  then,  h ,  the  distance  from  the  center  of 

wind  pressure  to  the  top  lateral  bracing,  is  7  +  2  =  9  feet; 

» 

and  b  is  6.5  feet.  Therefore, 

w  =  =  415  pounds  per  linear  foot 

6.5 

The  moments  due  to  a  uniform  load  of  1,330  pounds  per 
linear  foot  have  already  been  found;  those  due  to  a  uniform 
load  of  415  pounds  may  be  found  by  multiplying  the  former 
moments  by  iWo,  or  .31203.  The  results  are  as  follows: 


Location 


Moment,  in  Foot-Pounds 


Center 

20  feet  from  the  end 

15  feet  from  the  end 
■* 

10  feet  from  the  end 
5  feet  from  the  end 


.31203  X  484,900  =  151,300 
.31203  X  452,200  =  141,100 
.31203  X  389,000  =  121,400 
.31203  X  292,600  =  91,300 
.31203  X  162,900  =  50,800 


As  the  wind  pressure  under  consideration  is  that  on  a 
moving  train,  the  shears  will  be  found  as  for  a  moving  load, 
that  is,  by  loading  the  portion  of  the  span  on  one  side  of 
a  section.  They  are  as  follows: 

Location  Shear,  in  Pounds 


End 

5  feet  from  the  end 
10  feet  from  the  end 
15  feet  from  the  end 
20  feet  from  the  end 


415  X  54 

2 

11,200 

415  X  49  X  49 

2  X  54 

9,200 

415  X  44  X  44 

2  X  54 

7,400 

415  X  39  X  39 

2  X  54 

5,800 

415  X  34  X  34 

2  X  54 

4,400 

415  X  27  X  27 

2  X  54 

2,800 

Center 


§  70 


DESIGN  OF  PLATE  GIRDERS 


32.  Total  Moments  and  Shears.— As  the  dead  load, 
live  load,  impact  and  vibration,  and  wind  pressure  may  act 
simultaneously,  the  total  moments  and  shears  may  be  found 

0 

by  adding-  the  values  that  have  been  found  for  the  different 
conditions.  In  doing  so,  however,  it  must  be  remembered 
that  the  moments  and  shears  due  to  dead  load,  live  load, 
and  impact  and  vibration  have  been  found  for  the  load  on 
the  entire  width  of  track,  that  is,  on  two  girders,  while  those 
due  to  the  wind  pressure  are  the  effects  on  one  girder. 
Therefore,  to  find  the  total  moment  or  shear  at  any  section 
of  one  girder,  that  due  to  the  wind  pressure  may  be  added 
to  one-half  the  sum  of  those  due  to  dead  load,  live  load,  and 
impact  and  vibration,  as  just  found.  The  total  moments  and 
shears  on  each  girder  can  now  be  found. 

The  total  moments,  in  foot-pounds,  at  various  positions 
on  the  girder  are  as  follows: 

At  the  center, 

484,900  +_  2,702,500  +j , 290 jOO  +  15^300  =  2,890,200 

2 

At  20  feet  from  the  end, 

452,200  +  2,563,000  +  2,172,000  {  lii  m  =  2, 734, 700 

2 

At  15  feet  from  the  end, 

389,000  -f-  2,247,200  -f~  1,904,400  ^21  400  =  2  391  700 

2 

At  10  feet  from  the  end, 

292,600  +  1,703,700  +  1,443,800  +  9im  =  lj811>400 

2 

At  5  feet  from  the  end, 

162,900  +  976,900_+  827 jOO  +  50g00  =  ^ 034,700 
2 

The  total  shears,  in  pounds,  at  the  different  sections  of. 
the  girder  are: 

At  the  end, 

35,910  +  228,900  +  194,000-  +  1120Q  =  240,600 


28 


DESIGN  OF  PLATE  GIRDERS 


§76 


At  5  feet  from  the  end, 

29,260  +_195,400  +  165,600  +  9  200  =  204,300 
2 

At  10  feet  from  the  end, 

22,610  +  163,100  +  139,000  +  7400  =  169,800 
2 

At  15  feet  from  the  end, 

15,960  +  130,900  +  113,200  +  g  80Q 
2 

At  20  feet  from  the  end, 

9,310  +  101,600  +  89,100  4  40Q 

2  +  ’ 

At  the  center, 


=  135,800 


104,400 


0  ~t~  65,200  -f~  58,400  ^  ^  §qq 
2 


=  64,600 


33.  Design  of  Web. — A  i^e-inch  web  will  be  tried  first. 
The  gross  section  is  66  X  A  =  28.875  square  inches.  As 
the  total  shear  at  the  end  is  240,600  pounds,  the  intensity  of 
the  shearing  stress  is  240,600  -f-  28.875  =  8,330  pounds  per 
square  inch.  Consulting  Table  XXXVI,  finding  the  point 
on  the  curve  for  the  re-inch  web  corresponding  to  an  inten¬ 
sity  of  stress  of  8,330  pounds  per  square  inch,  and  looking 
horizontally  to  the  right,  it  is  found  that  the  stiffeners  must 
be  spaced  about  16  inches  apart.  According  to  B.  S.,  Art.  55, 
the  spacing  of  stiffeners  should  be  not  less  than  one-third 
the  depth  of  the  web.  In  this  case,  therefore,  the  stiffeners 
should  be  not  less  than  22  inches  apart.  As  the  spacing 
given  in  Table  XXXVI  is  16  inches,  it  is  necessary  to  try  a 
thicker  web.  A  web  i  inch  thick  will  be  tried  next.  The 
gross  section  is  66  X  i  =  33  square  inches,  and  the  intensity 
of  shearing  stress,  240,600  33  =  7,290  pounds  per  square 

inch.  Consulting  Table  XXXVI,  finding  the  point  on  the 
curve  for  the  i-inch  web  corresponding  to  an  intensity  of 
stress  of  7,290  pounds  per  square  inch,  and  looking  hori¬ 
zontally  to  the  right,  it  is  found  that  the  stiffeners  must 
be  spaced  22  inches  apart.  As  this  thickness  of  web  satis¬ 
fies  the  conditions  as  far  as  stiffener  spacing  at  the  end  is 


76 


DESIGN  OF  PLATE  GIRDERS 


29 


concerned,  the  required  spacing  of  stiffeners  at  other  sections 
will  next  be  found.  The  intensities  of  shearing  stress  are: 


Location 


Intensity  of 
Shearing  Stress, 
in  Pounds 
per  Square  Inch 


End 

5  feet  from  the  end 
10  feet  from  the  end 
15  feet  from  the  end 
20  feet  from  the  end 
Center  of  span 


240,600  -p  33  =  7,290 
204,300  -r  33  =  6,190 

169.800  +  33  =  5,150 

135.800  --  33  =  4,120 
104,400  -f-  33  =  3,160 

64,600  -f-  33  =  1,960 


34.  Spacing  of  Stiffeners. — Consulting  Table  XXXVI, 


finding  the  points  on  the  curve  for  i-inch  web  corresponding 
to  the  intensities  just  found,  and  looking  horizontally  to  the 
right  or  left  (whichever  is  nearer),  the  required  spacings  of 
stiffeners  are  found  to  be  as  follows: 

Spacing  of 

Location  Stiffeners, 

in  Inches 


End 

5  feet  from  the 
10  feet  from  the 
15  feet  from  the 
20  feet  from  the 
Center  of  span 


22 

end 

27 

end 

32 

end 

38 

end 

46 

62 

The  stiffener  spacing  at  other  points  on  the  girder  may 
be  found  by  interpolating  between  the  values  just  found. 
These  distances  will  not  give  the  actual  distances  between 
the  stiffeners,  but  simply  the  distances  that  must  not  be 
exceeded  at  the  various  sections.  The  actual  distances 
between  stiffener-s  depend  on  other  details,  such  as  rivet 
spacing,  and  are  usually  found  by  the  detailer  or  draftsman 
when  the  plans  are  being  made. 

35.  Pitch  of  Flange  Rivets. — The  required  spacing 
of  the  rivets  that  connect  the  flanges  to  the  web  at  any 
section  is  found  by  the  following  formula,  given  in  Desig?i  oi 
Plate  Girders ,  Part  1: 

.  Khr 


V 


30 


DESIGN  OF  PLATE  GIRDERS 


§76 


In  the  present  case,  the  rivets  are  in  double  shear  and  in 
bearing  on  the  i-inch  web-plate.  (They  are  also  in  bearing 
on  the  two  flange  angles,  but  it  may  be  assumed  that  the 
thickness  of  the  latter  is  greater  than  that  of  the  web;  it 
is  found  in  practice  that  this  is  invariably  true.  For  this 
reason,  the  bearing  on  the  flange  angles  need  not  be  con¬ 
sidered.)  The  rivets  used  in  deck  plate-girder  railroad 
bridges  are  i  inch  in  diameter  for  all  spans.  Those  in  the 
flanges  are  always  shop-driven  rivets  and,  according  to  B.  5., 
Art.  29,  the  values  in  Table  XL  will  be  used.  Consulting 
Table  XL,  the  value  of  one  f-inch  rivet  in  double  shear  is 
found  to  be  13,230  pounds,  and  in  bearing  on  a  plate  i  inch 

thick,  9,630  pounds. 
The  latter  value, 
being  the  smaller, 
must  be  used  in  the 
formula.  As  the 
flanges  have  not  yet 
been  designed,  it  is 
mot  known  what  size 
of  angles  will  be 
used,  so  that  the 
value  of  hr  cannot  be 
calculated.  In  actual 
practice,  however,  the  designer  soon  learns  what  sizes  of 
angles  are  generally  used  for  spans  of  different  lengths. 
In  the  type  of  bridge  now  under  consideration,  6"  X  6"  angles 
are  used  for  all  spans  up  to  about  70  feet,  and  8  in.  X  8  in. 
for  longer  spans.  In  the  present  case,  6"  X  6"  angles 
will  be  used.  Consulting  Table  XII,  it  is  found  that  there 
will  be  two  rows  of  rivets  in  each  leg,  the  line  midway 

between  the  two  rows  being  2i  -f  — -  —  3 1  inches  from  the 

A 


back  of  the  angle,  as  represented  in  Fig.  9.  The  distance 
between  the  backs  of  the  angles  in  the  flanges  has  already 
been  found  to  be  66]  inches.  The  distance  hr  is,  there¬ 
fore,  66i  —  3«  •—  3f  =  59|-  inches.  By  substituting  the 
proper  values  in  the  formula,  and  using  the  intensities  of 


§  7(5 


DESIGN  OF  PLATE  GIRDERS 


31 


shearing  stress  found  in  Art.  33,  the  following  pitches  are 
obtained: 


Location 

Rivet  Pitch,  in  Inches 

Bottom  Flange 

Top  Flange 

End 

9,630  X  59.5  0  Qo 

'  240,600  =  2'38; 

2.38  X  .9  =  2.14 

5  feet  from  the  end 

9,630  X  59.5  0  Qn. 

204,300  *  ’ 

2.80  X  .9  =  2.52 

10  feet  from  the  end 

9,630  X  59.5  0  on, 

169,800  ”  '  ’ 

3.37  X  .9  =  3.03 

15  feet  from  the  end 

9,630  X  59.5  _  ,  00. 
135,800 

4.22  X  .9  =  3.80 

20  feet  from  the  end 

9,630  X  59.5  . 

104,400  '  ’  ’ 

5.49  X  .9  -  4.94 

Center 

9,630  X  59.5  Q  Q7. 
64,600  ~  =  8'8/’ 

8.87  X  .9  =  7.98 

As  a  deck  railroad  bridge  is  under  consideration,  the  pitch 

K  h 

in  the  bottom  flange,  found  from  the  formula  p  =  — must 

be  multiplied  by  .9  to  get  the  required  pitch  in  the  top 
flange  (see  B.  A.,  Art.  57).  The  pitch  is  sometimes  made 
the  same  in  both  flanges,  that  found  for  the  top  flange  in 
the  manner  just  explained  being  used  for  the  bottom  as  well. 
As  in  the  case  of  stiffener  spacing,  the  foregoing  values 
will  not  represent  the  actual  spacing  of  rivets  at  any  section, 
but  simply  the  values  that  must  not  be  exceeded  at  the 
different  sections.  The  spacing  at  other  points  may  be 
found  by  interpolating  between  the  given  values.  As  the 
pitch  at  20  feet  from  the  end  came  out  greater  than  that 
allowed  in  B.  S.,  Art.  57,  there  was  no  necessity  for  com¬ 
puting  the  pitch  at  sections  nearer  the  center. 

36.  Design  of  Flanges. — The  required  area  of  cross- 
section  of  the  flanges  at  any  section  is  found  by  means  of 

the  formula  A  = - ~  ( Design  of  Plate  Girders ,  Part  1 ) . 

s  hg  8 

It  is  impossible  to  calculate  the  value  of  hs ,  as  the  areas  of 
the  flanges  are  not  yet  known;  for  a  first  trial,  however,  hs 
will  be  assumed  equal  to  the  depth  h  of  wA>,  the  flanges 


32 


DESIGN  OF  PLATE  GIRDERS 


76 


at  the  center  of  the  span  will  be  designed  on  this  basis,  using 
the  bending  moment  at  the  center  of  the  span,  and  the  dis¬ 
tance  hg  between  the  centers  of  gravity  of  the  trial  flanges 
will  be  computed.  With  this  corrected  value  for  hgy  the 
areas  of  the  flanges  will  again  be  found,  and  the  necessary 
correction  made.  It  will  seldom  be  found  necessary  to 
change  the  cross-section  of  the  flanges  as  found  by 
assuming  hg  =  h .  In  the  present  case,  h  =  66  inches, 
^  =  16,000  pounds,  and  /  =  i  inch.  To  apply  the  formula, 
the  bending  moment  already  found  must  be  multiplied  by  12, 
to  reduce  it  to  inch-pounds.  For  the  first  trial  cross-section 
at  the  center  of  the  span,  we  have,  therefore, 

=  28.72  square  inches 

This  is  the  value  for  the  gross  area  of  the  top  flange  and 
the  net  area  of  the  bottom  flange. 


37.  The  actual  choice  of  the  sizes  of  angles  and  plates  is 
wholly  a  matter  of  practice.  The  designer  usually  follows 
certain  established  rules  and  relies  to  a  great  extent  on  his 
experience.  It  is  considered  bad  practice  to  use  very  small 
or  thin  angles  and  a  large  number  of  plates.  It  is  also  con¬ 
sidered  bad  practice  to  make  the  entire  flange  section  of 
angles;  this  is  not  economical,  as  the  entire  section  of  flange 
must  be  continued  the  whole  length  of  the  girder.  In  B.  S., 
Art.  59,  it  is  required  that  one-third  to  one-half  the  flange 
area  shall  be  composed  of  angles.  In  the  present  case,  that 


. ,  .  ,  28.72  q  „  .  28.72  -  .  oc 

would  require  from  — - — ,  or  9.57,  to  — - — ,  or  14.36,  square 


3 


inches  in  two  angles,  or,  as  there  are  two  angles,  4.79  to 
7.18  square  inches  in  each  angle.  6"  X  6"  angles  with  thick¬ 
nesses  from  i  to  yi  inch  are  commonly  used  in  the  flanges 
of  plate  girders  for  railroad  bridges  up  to  about  70  feet  in 
length;  the  flange  plates  are  never  narrower  than  the  total 
width  of  the  two  flange  angles  together  with  the  thickness 
of  the  web,  nor  thicker  than  the  flange  angles.  In  the  pres¬ 
ent  case,  the  following  sections  will  be  used: 


DESIGN  OF  PLATE  GIRDERS 


33 


76 


Top  Flange  c  Secti°? *  IN 

Square  Inches 

Two  angles  6  in.  X  6  in.  X  i  in.  @  5.75  .  1  1.5 

One  plate  14  in.  X  I  in .  5.2  5 

One  plate  14  in.  X  tV  in .  6.1  2  5 

One  plate  14  in.  X  tV  in.  . .  6.1  2  5 

\ _ 

Total  gross  area  . . 2  9.0 


In  B.  S.,  Art.  60,  it  is  required  that,  when  plates  of  dif¬ 
ferent  thicknesses  are  used,  they  shall  diminish  in  thickness 
outwards  from  the  flange  angles.  An  exception  is  sometimes 
made  to  this  rule,  and  will  be  made  in  this  case,  when  it  is 
required  that  one  plate  shall  extend  the  full  length  of  the  top 
flange.  This  is  done  to  keep  water  and  dirt  from  working 
down  between  the  flange  angles  and  the  web,  and  to  give 
the  girder  a  better  finish.  A  thin  plate  serves  the  purpose 
just  as  well  as  a  thicker  |  d 

one,  and  is  more  eco-  1  .  -Iq—IIq  q  --  Q-  —  -  -3^ 

nomical,  as  all  that 
part  beyond  its  theo- 


-©- 


-e- 


-0- 


-e- 


-e- 


-0- 


-q — o- 


-0- 


H0- 


-0- 


-0- 


3 


0— 1  -0 - 0 - 0- 


-0- 


(C) 


•  j  i  - 0 - 0 - 0 - 0 - 0 - 0 - 0- 

retical  end  is  wasted,  / - - , - y~-~; 

r  (a) 

so  far  as  necessary 
flange  section  is  con¬ 
cerned. 

For  the  bottom 
flange  it  is  necessary 
to  deduct  from  the 
gross  section  the  areas 
of  cross-section  of  the 
rivet  holes.  This  is  most  easily  done  by  deducting  from 
each  angle  and  plate  the  holes  that  are  in  the  plate.  Fig.  10 
shows  the  method  of  riveting  flange  angles  to  the  web  and 
the  flange  plates  to  the  angles.  Each  rivet  d  in  the  hori¬ 
zontal  leg  of  any  angle  is  directly  opposite  one  e  in  the  ver¬ 
tical  leg;  this  brings  two  rivets  <7,  d  directly  opposite  each 
other  in  each  plate.  There  are  then  two  holes  to  be 
deducted  from  each  angle  and  two  from  each  plate.  The 
following  sections  will  be  used; 


34 


DESIGN  OF  PLATE  GIRDERS 


§76 


t,  Section,  in 

Bottom  Flange  Square  ItJches 

Two  angles  6  in.  X  6  in.  X  h  in.;  11.50  —  2  X  2  X  .50  = 
One  plate  16  in.  X  i  in. 

7 


One  plate  16  in.  X  Te  in. 
One  plate  16  in.  X  tq  in. 


8.0  —  2  X  .5  = 

7.0  -  2  X  .4375  = 

7.0  -  2  X  .4375  = 


9.5  0 
7.0  0 
6.1  2  5 
6.1  2  5 


Total  net  area,  2  8.7  5 


<t> 


<0 


JN 

<o 


38.  In  the  foregoing  design,  hs  was  assumed.  The  loca¬ 
tion  of  the  center  of  gravity  of  each  flange  and  the  distance 

,  between  the  two  cen¬ 
ters  of  gravity  will 
now  be  computed, 
and  the  design  of 

the  flanges  altered  if 

/ 

necessary.  For  the 


T 


i4X- 


/4*1S 


2  Ls  6*6 


XJ 


-t - i 

Center  of  Gravity  ' 


J3 

N 

1 


\J 

Fig.  11 


r r\ 


T 

& 

v 


2Ls6‘*6’*j 

Center  of  Gravity j  J 


center  of  gravity  of 
the  lower  flange, 
the  statical  moment 
for  each  angle  will  be 
taken  equal  to  the  area  of  net  section  multiplied  by  the  lever 
arm  of  the  gross  section,  as  the  position  of  the  center  of 
gravity  is  practically  the  same  for  both  sections.  The  posi¬ 
tion  of  the  center  of 
gravity  of  the  gross 
section  is  taken  from 
Table  IX.  Moments 
will  be  taken  about 
the  outer  edge  of  the 
section  in  each  case; 
the  lever  arms  for  the 
top  flange  are  shown 

in  Fig.  11,  those  for  the  bottom  flange  in  Fig.  12. 

The  statical  moments  for  the  top  flange  are  as  follows: 

6.1  2  5  X  .2188  =  1.3  4  0 

6.1  2  5  X  .6562  =  4.0  1  9 

5.2  5  X  1.0625  =  5.5  7  8 

1  1.5  X  2.93  =  3  3.6  9  5 


*  /  • 
/6  »  i 


o> 


r,  y  // 

'6*  fc 

'!  -y  n 

/6*% 


T 

s 

•*> 


I 


TT 

<c> 

Cv 


Fig.  12 


Oy 

* 


2  9.0 


4  4.6  3  2 


§76 


DESIGN  OF  PLATE  GIRDERS 


35 


The  distance  of  the  center  of  gravity  of  the  top  flange  is, 
therefore,  44.632  -f-  29  =  1.54  inches  from  the  outside  of  the 
section.  As  the  plates  have  a  total  thickness  of  tV  +  h  +  t 
=  1.25  inches,  the  center  of  gravity  of  the  top  flange  is 
1.54  —  1.25  =  .29  inch  below  the  back  of  the  angles. 

The  statical  moments  for  the  bottom  flange  are  as  follows: 

6.1  2  5  X  .2188  =  1.3  4  0 

6.1  2  5  X  .6562  =  4.0  1  9 

7.0  X  1.125  =  7.8  7  5 

9.5  0  X  3.05  =  2  8.9  7  5 

2  8.7  5  4  2.2  0  9 


The  distance  of  the  center  of  gravity  of  this  flange  from 
the  outside  edge  of  the  flange  is,  therefore,  42.209  28.75 

=  1.468  inches  from  the  outside  of  the  section.  As  the 
plates  have  a  total  thickness  of  -£■  +  ts- -h-Te  =  1.375  inches, 
the  center  of  gravity  of  the  bottom  flange  is  1.468  —  1.375 
=  .09  inch  from  the  back  of  the  angles. 

As  the  distance  back  to  back  of  the  flange  angles  is 
66.25  inches,  the  distance  hg  between  the  centers  of  gravity 
of  flanges  is  66.25  —  .29  —  .09  =  65.87  inches.  This  is  very 
nearly  equal  to  the  assumed  distance  of  66  inches.  Substi¬ 
tuting  this  value  of  he  in  the  formula  for  area,  the  result  is 


A  =  2’890’2— -  i  X  2  X  66  =  32.91  -  4.12 
65.87  X  16,000 

—  28.79  square  inches 

This  is  slightly  greater  than  the  net  area  of  the  trial  bottom 
flange,  but  the  difference  is  so  slight  (.04  square  inch)  that 
it  is  inadvisable  to  make  any  changes.  Had  the  difference 
been  greater — say,  .2  or  .3  square  inch — it  might  have  been 
advisable  to  increase  the  thickness  of  one  of  the  flange  plates 
by  tV  inch. 


It  will  be  seen  that  the  flange  plates  are  wider  and  thicker 
in  the  lower  flange  than  in  the  upper.  They  are  sometimes 
made  the  same  width,  in  which  case  the  lower  flange  plates 
must  be  still  thicker,  or  else  more  plates  must  be  used. 
If  those  in  the  lower  flange  are  made  about  2  inches  wider 
than  those  in  the  top,  and  the  same  number  of  plates  is 


38 


DESIGN  OF  PLATE  GIRDERS 


78 


used,  it  will  usually  be  found  that  the  theoretical  lengths 
of  corresponding  plates  in  the  two  flanges  are  the  same 
or  very  nearly  so;  this  condition  is  very  convenient  in 
designing,  especially  if  the  same  rivet  spacing  is  used  in 
both  flanges. 

Some  engineers  do  not  design  the  top  flange,  but  make  it 
the  same  size  as  the  lower  flange.  This  gives  additional 
section,  and  therefore  additional  strength  to  the  top  flange, 
but  is  not  economical.  If  this  were  done  in  the  present 
case,  as  the  gross  area  of  the  lower  flange  is  11.50  +  84-7+7 
=  33.5  square  inches,  and  the  required  gross  area  of  the 
upper  flange  is  28.79  square  inches,  the  difference,  which 
is  4.71  square  inches,  would  be  wasted  in  the  upper  flange. 
Unless  it  is  stated  in  the  specifications  that  both  flanges 
must  have  the  same  gross  area,  they  should  be  designed 
separately. 

39.  Lengths  of  Flange  Plates. — The  flange  angles  in 
both  flanges  and  the  plate  next  to  the  flange  angles  in  the 
top  flange  are  continued  the  full  length  of  the  girder.  The 
other  plates  are  cut  off  where  they  fare  no  longer  needed. 
For  this  purpose,  the  areas  required  at  the  different  sections 
at  which  the  moments  have  been  computed  will  be  deter¬ 
mined,  and  the  curves  of  flange  areas  will  be  plotted.  The 
distances  between  the  centers  of  gravity  of  the  flanges  at 
sections  other  than  at  the  center  are  not  known,  but  they 
may  be  assumed  for  trial  equal  to  that  at  the  center,  and 
corrected  later.  Using  the  bending  moments  found  in 
Art.  32,  the  required  flange  areas,  in  square  inches,  are: 

At  the  center, 


2,890,200  X  12 
65.87  X  16,000 


4.12  =  32.91  -  4.12  =  28.79 


At  20  feet  from  the  end, 


2,734,700  X  12 
65.87  X  16,000 


-  4.12  =  31.15  -  4.12  =  27.03 


At  15  feet  from  the  end, 


2,391,700  X  12 
65.87  X  16,000 


-  4.12  =  27.24  -  4.12  =  23.12 


§76 


DESIGN  OF  PLATE  GIRDERS 


37 


At  10  feet  from  the  end, 

h8^’40LXin  -  4-12  =  20.63  -  4'12 
65.87  X  16,000 

At  5  feet  from  the  end, 

1,034,700  X  12 


16.51 


65.87  X  16,000  4.12=11.79-4.12=  7.67 

Fig-.  13  shows  the  curves  of  flange  areas:  AB  represents 
the  half  span;  C,  D ,  E,  and  E ,  the  sections  at  5,  10,  15,  and 
20  feet  from  A ,  respectively;  C  C' ,  D  D' ,  E  £',  EE',  and  B  B' , 


the  required  areas  of  the  flanges  at  C,  D ,  E ,  F,  and  B,  respect- 

th 

ively,  B  L  and  B  L'  representing  — ,  or  the  portion  of  web 

8 

that  is  included  in  flange  area;  L  Lx,  LXL*,  A2A3,  and  A3A4, 
the  areas  of  the  angles  and  plates  in  the  upper  flange;  and 
L’  L,' ,  A/  LJ ,  LJ ,  and  LJ  LJ ,  the  areas  of  the  angles  and 
plates  in  the  lower  flange.  Dotted  curves  are  then  drawn 
through  A,  C’ ,  D' ,  E' ,  F',  and  B'.  Drawing  lines  through 
L ,  Lx,  A2,  etc.,  and  noting  where  they  intersect  the  curves, 
the  points  at  which  the  plates  are  no  longer  required  are 
determined.  At  C ,  no  plates  are  required;  at  D,  one  plate 
on  each  flange  is.  required;  at  E ,  two  plates  on  each  flange 
are  required;  and  at  F  and  B ,  three  plates  on  each  flange  are 
required.  At  F  and  B  there  is  no  need  to  revise  the  flange 


38 


DESIGN  OF  PLATE  GIRDERS 


§76 


area,  as  the  entire  section  is  required.  In  some  cases,  as 
at  E,  the  end  of  a  plate  is  just  included  in  the  section,  but, 
as  the  plate  at  that  point  does  not  carry  much  stress,  it 
should  not  be  counted  as  part  of  the  flange  area  in  calcu¬ 
lating  the  distance  between  the  centers  of  gravity  of  the 
flanges. 

The  actual  location  of  the  center  of  gravity  at  each  section 
can  be  calculated  in  the  same  way  as  in  Art.  38  for  the  entire 
flange;  it  is  not  necessary  to  repeat  the  numerical  steps. 
They  are,  for  the  top  flange,  .64  inch  at  E ,  1.09  inches 
at  D,  1.68  inches  at  C,  below  the  backs  of  the  flange  angles; 
and  for  the  bottom  flange,  .43  inch  at  Ef  .86  inch  at  D , 
and  1.68  inches  at  C,  above  the  backs  of  the  flange 
angles.  The  distances  between  the  centers  of  gravity  of 
the  flanges  are: 


At  E,  66.25  —  .64  —  .43  =  65.18  inches 

At  A  66.25  -  1.09  -  ;86  =  64.30  inches 

At  C,  66.25  -  1.68  -  1.68  =  62.89  inches 


The  revised  flange  areas,  in  square  inches,  are,  therefore, 
as  follows: 

At  15  feet  from  the  end, 


2,391,700  X  12 


65.18  X  16,000 
At  10  feet  from  the  end, 
1,811,400  X  12  _  4  12 
64.30  X  16,000 
At  5  feet  from  the  end, 
1,034,700  X  12 


-  4.12  =  27.52  -  4.12  =  23.40 


=  21.13  -  4.12  =  17.01 


„  _  4.12  =  12.34  —  4.12  =  8.22 

62.89  X  16,000 

The  curve  of  flange  areas  may  now  be  corrected  by  plotting 
these  values  at  C,  D,  and  Ey  drawing  the  curves  shown  in  full 
lines,  and  locating  the  theoretical  ends  of  the  flange  plates. 
The  distance  scaled  from  the  theoretical  end  of  a  plate  to  the 
center  line  is  one-half  the  length  of  plate;  in  this  case,  the 
theoretical  lengths  of  plates  in  the  top  flange  are  approxi¬ 
mately  25,  34.5,  and  40.5  feet,  and  in  the  bottom  flange,  25.5, 
34.75,  and  43  feet.  According  to  />.  S.,  Art.  f>0,  each  plate 


§76 


DESIGN  OF  PLATE  GIRDERS 


39 


shall  extend  12  inches  at  each  end  beyond  the  theoretical  end; 
this  will  increase  the  length  of  each  plate  by  2  feet.  The 
first  plate  in  the  top  flange  and  all  the  angles  will  continue 
the  full  length  of  the  girder,  that  is,  55  feet  10  inches.  The 
flanges  are  then  made  up  as  follows: 

Top  Flange 

Two  angles  6  in.  X  6  in.  X  i  in.  X  55  ft.  10  in 

One  plate  14  in.  X  "o  in.  X  55  ft.  10  in. 

One  plate  14  in.  X  A  in.  X  36  ft.  6  in. 

One  plate  14  in.  X  iV  in.  X  27  ft. 

Bottom  Flange 

Two  angles  6  in.  X  6  in.  X  i  in.  X  55  ft.  10  in. 

One  plate  16  in.  X  i  in.  X  45  ft. 

One  plate  16  in.  X  tV  in.  X  36  ft.  9  in. 

One  plate  16  in.  X  tV  in.  X  27  ft.  6  in. 

The  actual  lengths  of  the  plates  will  probably  be  slightly 
different  from  the  lengths  given,  the  difference  being  due  to 
rivet  spacing  in  the  flanges. 

40.  Splices. — As  no  plate  or  angle  is  longer  than 
70  feet,  it  is  unnecessary  to  splice  any  flange  member 
(B.  S.,  Art.  61).  Consulting  Table  V,  it  is  found  that  the 
longest  plate  66  in.  X  i  in.  that  it  is  possible  to  get  is 
34  feet  long;,  it  is  therefore  necessary  to  splice  the  web.  It 
will  be  spliced  at  the  center, '  making  each  half  27  feet 
11  inches  long,  nearly.  The  size  of  the  splice  plates  will 
first  be  determined.  Consulting  Table  XI,  it  is  found  that 
for  a  6"  X  6"  X  i''  angle  the  nominal  and  actual  widths  are 
equal;  then,  the  actual  size  of  the  leg  of  a  6"  X  6"  X  i" 
angle  is  6i  inches.  As  the  distance  back  to  back  of  the 
flange  angles  is  66i  inches,  the  clear  distance  between  the 
vertical  legs  is  66i  —  6i  —  6i  =  54  inches.  Allowing  i  inch 
clearance  at  top  and  bottom  leaves  53f  inches  as  the  height 
of  the  splice  plate.  According  to  B.  S.,  Art.  56,  each 
splice  plate  shall  have  a  sectional  area  equal  to  75  per 
cent,  that  of  the  web.  In  the  present  case,  that  of  the  web 
is  33  square  inches;  then,  the  area  of  each  plate  must 
be  .75  X  33  =  24.75  square  inches.  As  the  plates  are 


40 


DESIGN  OF  PLATE  GIRDERS 


76 


53f  inches  deep,  the  required  thickness  is  24.75  -f-  53.75 
=  .46  inch.  The  nearest  standard  thickness  is  1  inch;  then, 
each  splice  plate  will  be  531  in.  X  h  in.  A  spacing  of  rivets 

will  now  be  assumed;  if  it 
gives  sufficient  resistance,  it 
will  be  used;  if  not,  the  num¬ 
ber  of  rivets  will  be  increased. 
The  spacing  shown  in  Fig.  14 
will  be  assumed. 

The  rivets  are  in  double 
shear  and  in  bearing  on  a  1-inch 
web-plate.  It  has  already  been 
found  (Art.  35)  that  the  latter 
gives  the  smaller  value  for  a 
l-inch  rivet;  this  value  is  9,630 
pounds.  As  the  distances  of 
the  rivets  from  the  neutral  axis 
are  2,  6,  10,  13,  16,  19,  22,  and 
25s  inches,  and  as  there  are 
four  rivets  at  each  of  these 
distances,  the  moment  of  re¬ 
sistance  of  the  rivets  is,  accord¬ 
ing  to  the  formula  given  in  Design  of  Plate  Girders,  Part  1, 
9,630  X  4  X  (2*  +  62  +  102  +  132  +  162  +  19*  -f  22*  +  25.1252) 

25.125 


Pig.  14 


=  3,130,000  inch-pounds 

The  moment  that  the  web  can  bear  is  given  by  the  formula 

s  t  hi 


M  = 


8 


( Design  of  Plate  Girders ,  Part  1).  In  the  present 


case,  the  value  of  s  for  bending  stress  is  16,000  pounds  per 
square  inch,  t  =  i  inch,  and  h  —  66  inches;  then, 


M  = 


16,000  X  .5  X  662 

8 


4,356,000  inch-pounds 


Since  this  is  greater  than  the  resisting  moment  that  has 
been  found,  it  is  necessary  to  use  more  rivets.  As  the  rivets 
farthest  from  the  neutral  axis  are  the  most  effective,  we 
shall  begin  another  row  outside  of  the  first  two  rows,  and 
first  compute  the  moment  of  resistance  of  a  few  rivets  near 


76 


DESIGN  OF  PLATE  GIRDERS 


41  * 


the  flanges.  Let  us  first  try  two  rivets  at  the  top  and  two  at 
the  bottom,  at  distances  of  25.125  and  22  inches  from  the 
neutral  axis.  The  moment  of  resistance  of  these  four 
rivets  is 

9,630  X  (22s  +  25.125s) 


2  X 


855,000  inch-pounds, 


o 


o 


o 


o 

o 

o 

1° 

o 

o 

o 

o 

o 

j!° 

o 

o 

o 

o 

o 

:!  ° 

o 

o 

o 

o 

o 

o 

O  tjO 

o  !i  o 

o 

o 

o 

a 

o 


o 


25.125  * 

which,  added  to  that  already  found,  gives  3,130,000  +  855,000 
=  3,985,000  inch-pounds.  This  is  still  too  small.  Let  us  try 
one  more  rivet  at  the  top  and  one  at  the  bottom  in  the  same 
row,  each  19  inches  from  the  neutral  axis.  The  moment  of 
resistance  of  these  two  is 

2  X  Myxljg  =  277,000  inch-pounds, 

20. 125 

which,  added  to  that  already  found,  gives  3,985,000  +  277,000 
=  4,262,000  inch-pounds.  This  is  still  too  small.  Let  us  try 
one  more  rivet  at  the  top  and  one  more  at  the  bottom  in  the 
same  row,  each  16  inches 
from  the  neutral  axis.  The 
moment  of  resistance  of 
these  two  is 

O  ..  9,630  X  16s 
X  25.125 

=  196,000  inch-pounds, 
which,  added  to  that  already 
found,  gives  4,262,000 
+  196,000  =  4,458,000 
inch-pounds.  This  is  a 
little  larger  than  the  mo¬ 
ment  of  the  web,  and  is, 
therefore,  sufficient.  Three 
splice  plates  on  each  side 
of  the  web  will  now  be  used 
instead  of  one,  the  top  and 
bottom  plates  having  three 
rows  of  rivets  on  each  side 
of  the  splice  and  the  middle  plate  two  rows.  It  is  neces¬ 
sary  to  rearrange  the  spacing  of  the  rivets,  so  that  there 
will  be  the  proper  distance  from  the  edge  of  each  plate  to 

135-11 


Pig.  15 


42 


DESIGN  OF  PLATE  GIRDERS 


§76 


the  nearest  rivet,  and  i  inch  clearance  between  the  plates 
(see  B.  S.,  Art.  41).  The  spacing:  represented  in  Fig:.  15 
will  be  used;  this  changes  the  location  of  the  rivets,  and  it  is 
well  to  recompute  the  moment  of  resistance  of  the  rivets  in 
the  entire  splice.  That  moment  is  as  follows:  M  =  9,630 
X  [4  X  (22  +  5.52  +  92  +  12.52)  +  6  X  (16.1252  +  19.125* 
+  22.1252  +  25.1252)]  -r  25.125  =  4,433,000  inch-pounds, 
which  is  larger  than  the  moment  of  resistance  of  the  web,  and 
therefore  sufficient.  It  is  unnecessary  to  calculate  the  moment 
of  resistance  of  the  splice  plates;  if  the  plates  on  each  side  have 
an  area  on  a  vertical  section  75  per  cent,  that  of  the  web,  their 
moment  of  resistance  will  be  greater  than  that  of  the  web. 


41.  Bearings. — Since  the  abutments  are  granite,  for 
which,  according  to  B.  S.,  Art.  29,  the  allowable  intensity 
of  pressure  is  500'  pounds  per  square  inch,  and  the  end 
shear,  which  is  equal  to  the  reaction,  is  240,600  pounds,  the 
required  area  of  bearing  is  240 ,,600  500  «=  481.2  square 

inches.  In  Art.  26,  it  was  stated  that  the  bedplates  would 
be  made  22  inches  long;  the  required  width  is,  therefore, 
481.2  -h  22  =  21.9  inches.  They  will  be  made  22  inches  long. 


42.  End  Stiffeners. — The  formula  given  in  Design  of 
Plate  Girders ,  Part  1,  for  the  required  thickness  of  end  stif- 

R 


feners  is  t’ 


In  the  present  case,  R  =  240,600 


nsb  ( b  —  2) 

pounds,  and,  according  to  B.  S.y  Art.  29,  the  allowable 
intensity  of  bearing  is  18,000  pounds  per  square  inch. 
The  outstanding  legs  of  the  flange  angles  are  6  inches  wide; 
then,  according  to  B.  S.,  Art.  55,  the  stiffeners  will  be 
5  in.  X  3i  in.  It  will  first  be  assumed  that  there  are  four 
stiffeners;  this  gives 

240,600 


t’  = 


=  .743  inch 


4  X  18,000  X  (5  -  i) 

'  When  the  required  thickness  of  stiffeners  comes  out 
greater  than  f  inch,  as  in  this  case,  it  is  generally  con¬ 
sidered  advisable  to  use  more  stiffeners.  Using  eight  gives 
„  240,600 


8  X  18,000  X  (5  -i) 


=  .371  inch,  say,  f  inch 


DESIGN  OF  PLATE  GIRDERS 


43 


As  this  thickness  is  less  than  f  inch,  it  will  be  adopted,  and 
eight  stiffeners  5  in.  X  3i  in.  X  f  in.  with  reinforcing  plates 
under  them  will  b.e  used.  The  stiffeners  will  be  riveted  to 
the  girder  with  i-inch  rivets.  The  value  in  single  shear, 
6,610  pounds  (Table  XL),  is  found  to  be  the  smallest 
value.  Then,  the  number  of  rivets  required  to  connect  each 
stiffener  is 


240,600 
8  X  6,601 


4.55,  or,  say,  5  rivets 


43.  Lateral  System. — The  lateral  truss  represented  in 
Fig.  16  will  be  used  for  both  the  upper  and  the  lower  flange; 
the  end  frames  will  be  about  52  feet  apart,  which  makes  it 
possible  to  use  eight  panels  at  6  feet  6  inches  each.  The 
wind  load  is  given  in  B.  S .,  Art.  27.  The  pressure  on  the 
lower  half  of  the  girder,  about  3  feet  in  depth,  is  resisted  by 
the  lower  laterals;  the  pressure  of  50  pounds  per  square  foot, 
or,  in  this  case,  3  X  50  —  150  pounds  per  linear  foot,  evi¬ 
dently  causes  the  greatest  stresses  in  the  lower  lateral  truss. 


Then,  the  panel  load  for  the  lower  lateral  truss  is  150  X  6.5 
=  975  pounds.  The  pressure  on  the  upper  half  of  the 
girder,  and  on  the  rails  and  ties,  say  4  feet  in  depth,  together 
with  the  pressure  of  300  pounds  per  linear  foot  on  the  train, 
are  resisted  by  the  upper  lateral  system.  The  pressure  on 
the  train — together  with  30  pounds  per  square  foot,  or 
4  x  30  =  120  pounds  per  linear  .foot  on  the  girders,  ties, 
and  rails — evidently  causes  greater  stresses  than  50  pounds 
per  square  foot  on  the  girders,  ties,  and  rails  alone.  The 
live  wind  panel  load  for  the  upper  lateral  system  is,  there¬ 
fore,  300  X  6.5  —  1,950  pounds,  and  the  dead  wind  panel 
load,  120  X  6.5  =  780  pounds. 


44  DESIGN  OF  PLATE  GIRDERS  §76 

44.  The  end  panel  of  the  upper  lateral  truss  will  first 

be  considered.  The  live-load  shear  is  ^>950  X  7  _  gg25 

z 

780  x  7 

pounds,  and  the  clead-load  shear  is  - — — - =  2,730  pounds. 

A 

The  total  shear  is,  therefore,  6,825  +  2,730  =  9,555  pounds. 
The  panel  length  is  the  same  as  the  distance  center  to.  center 
of  girders;  so  the  inclination  of  the  laterals  is  about  45°; 
esc  45°  =  1.414.  The  direct  stress  in  the  diagonal  is  9,555 
X  1.414  —  13,510  pounds,  tension  when  the  wind  blows  in 
one  direction,  and  compression  when  in  the  other  direction. 
According  to  B.  S.,  Art.  34,  the  member  must  be  designed 
for  13,510  +  .8  X  13,510  =  24,320  pounds  tension  and  com¬ 
pression.  Dividing  by  16,000  gives  24,320  -r-  16,000  =  1.52 
square  inches  net  section  required  to  resist  the  tension. 


45.  According  to  B.  S.,  Art.  86,  the  smallest  angle 
that  can  be  used  for  lateral  bracing  is  3i  in.  X  3i  in.  X  I  in. 
In  Table  IX  the  gross  area  of  this  angle  is  given  as 
2.48  square  inches.  The  number  of  holes  to  be  deducted 
depends  on  the  method  of  riveting  the  angle  to  the  con- 
,//  nection  plate.  Fig.  17 

Y  i 


l  of  era/  Xngfe  3^  X  3 $  X  g 


Log  /\ng/e3j>  X3%X  § 


shows  a  connection 
frequently  used:  the 
short  angle  a  riveted 
to  the  main  angle  at 
the  end  is  called  a  lug 
angle,  and  serves  the 
purpose  of  transmit¬ 
ting  the  stress  from 
the  leg  b  of  the  main 
angle  to  the  connec¬ 
tion  plates.  In  practice,  the  number  of  rivets  connecting  the 
two  angles  is  usually  made  one  more  than  half  the  number 
required  to  connect  the  lateral  to  the  connection  plate. 
With  rivets  spaced  as  shown,  1.5  holes  must  be  deducted, 
according  to  B.  S.,  Art.  33.  As  the  angle  is  f  inch  thick, 
the  area  of  cross-section  of  one  hole  is  .375,  and  of  1.5  holes, 


10  0 


Fig.  17 


§76 


DESIGN  OF  PLATE  GIRDERS 


45 


1.5  X  .375  =  .5625  square  inch.  Deducting  this  from  2.48 
leaves  1.92  square  inches  net  section.  As  only  1.52  is 
required,  this  angle  is  large  enough  so  far  as  tension  is 
concerned. 

46.  The  distance  center  to  center  of  girders,  measured 
along  a  diagonal,  is  6.5  X  1.414  —  9.19  feet  =  110  inches, 
nearly.  The  ends  of  the  laterals  are  riveted  to  the  con¬ 
nection  plates,  so  that  the  unsupported  length  may  be  taken 
as  the  distance  between  connections,  or  about  18  inches  at 
each  end  shorter  than  the  distance  between  girders,  leaving 
110  —  2  X  18  =  74  inches  unsupported.  Table  IX  gives  the 
least  radius  of  gyration  as  .68  inch;  then, 

/  74 

-  =  =  108.82 
r  .68 

Table  XXXV  gives  the  allowable  intensity  of  compressive 
stress  as  9,650  pounds;  as  the  gross  area  is  2.48  square 
inches,  the  strength  of  the  angle  is  2.48  X  9,650  =  23,930 
pounds.  This  is  very  nearly  equal  to  24,320,  the  required 
strength,  and  so  this  angle  is  sufficiently  large. 

47.  As  the  span  under  consideration  is  less  than  75  feet 
long,  it  will  be  shipped  riveted  up  complete.  That  is,  the 
rivets  connecting  the  laterals  to  the  lateral  plates  will  be 
shop-driven,  and,  according  to  B.  S.,  Art.  29,  the  values 
given  in  Table  XL  will  be  used.  Table  XL  gives  the  value 
of  a  |--inch  rivet  in  single  shear  as  6,610  pounds;  the  required 
number  of  rivets  is  then  24,320  -f-  6,610  =,  3.7,  or,  say, 
4  rivets.  As  the  3i"  X  3i"  X  t"  angle  is  strong  enough  in 
the  end  panel  of  the  upper 
lateral  system,  it  is  sufficient 
in  all  other  panels,  and  so 
there  is  no  need  in  this  case 
of  making  any  computations 
for  the  other  angles. 

48.  The  amount  of  wind 
pressure  that  is  transmitted 
to  the  abutments  by  the  end 
frames  (a  diagram  of  which  is  shown  in  Fig.  18)  can  be  found 


40 


DESIGN  OF  PLATE  GIRDERS 


§  70 


by  multiplying  the  sum  of  the  live  and  dead  wind  loads  per 

linear  foot  on  the  upper  lateral  truss  (300  -f  120  =  420  pounds) 

by  the  total  length  of  the  girder,  which  is  55  feet  10  inches, 

or  55.83  feet.  As  one-half  of  this  load  is  transmitted  by  each 

(  f  •  420  X  55.8333  11  7Qr  •,  A 

frame,  the  amount  is - - -  =  11,/ 25  pounds.  As 

A 

there  are  two  diagonals,  one  will  be  assumed  to  be  out  of 
action  when  the  other  is  in  tension.  The  height  of  the  frame 
is  about  4.5  feet;  the  tension  in  a  diagonal  is,  therefore, 

11,725  X  AA±J—  =  11,725  X  ~  =  14,230  pounds 
6.5  6.5 

It  has  already  been  found  that  a  34"  X  34"  X  t"  angle  is 
more  than  sufficient  for  a  stress  in  tension  of  24,320  pounds; 
so  that  it  will  be  used  in  this  case. 


DESIGN  OF  A  HIGHWAY 
TRUSS  BRIDGE 

(PART  1) 


GENERAL  FEATURES 

«* 

1.  General  Data. — The  principles  of  design,  as  applied 
to  through  pin-connected  highway  bridges,  will  be  illustrated 
by  the  complete  design  of  a  bridge  of  this  type.  The  bridge 
will  be  designed  in  conformity  with  the  following  general 
data,  and  according  to  the  specifications  given  in  B.  S* 

GENERAL  DATA 

For  bridge  over  Lackawanna  River _ _ _ _ 

at _ Scranton ,  Pennsylvania _  _ 

Length  and  general  dimensions  ® ne  sPan  160  ^eel  center  to 
center  of  bearings 

Skew  or  angle  of  abutments  with  center  line  of  bridge 
Width  of  bridge  and  location  of  trusses  ^  sidewalks,  6  feet 
clear  width;  one  roadway  25  feet  between  w heel-guards.  Trusses 
located  between  sidewalks  and  roadway^ _ _ 

Floor  system  ®ne  ^ayer  oa&  plank  2  inches  thick;  one  layer 
3  inches*  thick.  Steel  stringers 


*The  abbreviation  B.  S.  stands  for  Bridge  Specifications ,  to  which 
Section  frequent  reference  is  made  in  this  and  in  some  of  the  fol¬ 
lowing  Sections.  All  tables  referred  to  are  found  in  Bridge  fables , 
unless  otherwise  stated. 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

§  77 


2 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


Number  and  location  of  tracks _ 0  nestrect-rai  Iway  track  at 

center  of  roadway _ 

As  given  in  B.  S.,  Art.  98  ( 2 )  and  (5) 


Cement-concrete  abutments 


Loading _ 

Description  of  abutments. 

Distance  from  floor  to  clearance  line _ Not  more  than  6  feet 

high  water _ ^  _ 


<  <  ( i 


<< 


(< 


{« 


<  < 


20  feet 


25  feet 


low  water _ 

<(  <(  <<  <<  -i 

river  bottom _ 

Character  of  river  bottom  * ee t  mud  and  Sl^i>  then 

solid  rock _ _ _ _ 

Usual  season  for  floods _ March  and  April  _ 

Name  of  nearest  railroad  station  Scranton ,  Pennsylvania 

Distance  to  nearest  railroad  station _ ojmzles _ _ 

Time  limit  ^  months  from  award  of  contract 


Name  of  Engineer. 


International  Textbook  Company 
Scranton ,  Pennsylvania 


Address  of  Engineer _ : _ 

Remarks  Bridge  to  have  ornamental  railing  3  feet  9  inches 
high  at  each  side  of  bridge.  The  top  of  bridge  seat  must  be  kept 
above  high-water  line 


2.  Plans. — The  plans  for  some  parts  of  this  bridge  are 
shown  in  Bridge  Drawing.  The  student  is  advised  to  consult 
those  plates  frequently  during  the  study  of  this  Section. 

3.  Kind  of  Bridge. — The  first  step  is  to  determine  the 


kind  of  bridge.  As  the  distance  from  the  floor  to  the  clear¬ 
ance  line  is  limited  to  6  feet,,  it  is  evident  that  a  through 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


3 


bridge  must  be  used,  there 
not  being  sufficient  room 
for  a  deck  bridge.  As  the 
span  is  160  feet,  pin-con¬ 
nected  trusses  must  be 
used  (B.  S.,  Art.  91 ):  Ac¬ 
cording  to  B.  S .,  Art.  229, 
panels  from  20  to  30  feet 
in  length  are  best  for  pin- 
connected  trusses:  eight 
panels  20  feet  long  will  be 
used.  If  a  simple  Pratt 
truss  is  chosen,  with  a 
depth  of  27  feet,  which  is 
about  one-sixth  of  the 
span,  the  angle  between 
the  inclined  web  members 
and  the  lower  chord  will 
be  about  53°  30k  This 
angle  is  greater  than  50°, 
as  required  in  B.  A.,  Art. 
92,  and  hence  a  depth  of 
27  feet  will  be  adopted. 
The  outline  of  the  truss  is 
shown  in  Fig.  1. 

4.  Width  of  Bridge. 
The  data  require  that  the 
trusses  shall  be  located 
between  the  roadway  and 
the  sidewalks,  and  that  the 
roadway  shall  have  a  clear 
width  of  25  feet  between 
wheel-guards.  According 
to  B.  S.}  Art.  125,  the 
edges  of  the  wheel-guards 
toward  the  roadway  will  be 
6  inches  from  the  clearance 


4 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


lines  of  the  trusses,  making  the  clear  distance  between  the 
latter  26  feet.  The  width  occupied  by  a  truss  depends 
on  the  width  of  the  widest  members;  for  pin-connected 
trusses  it  is  seldom  less  than  18  inches.  In  the  present  case, 
the  width  will  be  assumed  to  be  24  inches.  If  the  design 
works  out  more  or  less  than  this,  it  may  be  slightly  changed. 
With  a  width  of  2  feet  for  each  truss,  the  distance  center  to 
center  of  trusses  is  28  feet,  and  the  distance  between  the 
clearance  lines  of  the  trusses  toward  the  sidewalks  is  30  feet. 
As  the  data  require  2  sidewalks  6  feet  wide,  the  distance 
between  the  railings  will  be  30  +  6  +  6  =  42  feet.  Fig.  2 
shows  the  assumed  width  and  location  of  trusses  and  the 
location  of  railings.  _ 

DESIGN  OF  FLOOR  SYSTEM 

/ 


STRINGERS 

5.  Cross-Section  of  Floor. — The  cross-section  of  floor 
usually  employed  for  this  type  of  bridge  is  shown  in  Fig.  3. 
The  rails  h ,  h  for  the  street-railway  track  rest  on  6"  X  6"  ties 
8  feet  long,  marked^.  When  the  rails  are  the  same  height 
as  the  thickness  of  the  floor  plank,  the  lower  layer  of  plank 
is  spiked  directly  to  the  top  of  the  ties.  When,  as  assumed 
in  the  figure,  the  height  of  the  rail  is  greater  than  the  thick¬ 
ness  of  the  floor  plank,  longitudinal  nailing  pieces  /,  as 
required  in  B.  S .,  Art.  121,  are  spiked  to  the  top  of  the  ties, 
and  the  lower  layer  of  plank  is  spiked  to  the  nailing  pieces. 
For  the  remainder  of  the  roadway,  the  lower  layer  of  plank  d 
is  fastened  to  spiking  pieces  that  are  bolted  to  the  tops  of  the 
steel  beams.  The  upper  layer  c  is  then  spiked  to  the  top  of 
the  lower  layer. 

At  each  side  of  the  roadway,  6"  X  6"  wheel-guards  e  are 
bolted  to  the  top  of  the  lower  layer  of  plank;  and  the  side¬ 
walk  plank  by  for  which  one  layer  is  sufficient,  is  continued 
right  through  the  truss  out  over  the  wheel-guard.  The  side¬ 
walk  plank  is  supported  at  other  points  by  steel  beams  with 
spiking  pieces  on  top.  To  prevent  the  ends  of  the  sidewalk 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


5 


plank  b  and  the  edges  of  the  wheel-guards  e  from  being  worn 
by  the  wheels,  a  guard  angle  a ,  usually  2i  in.  X  in.  X  i  in., 
is  fastened  by  screws  to  the  ends  of  the  sidewalk  plank,  as 
shown  in  Fig.  4. 

It  is  customary,  in  order  to  facilitate  drainage,  to  make  the 
sides  of  the  roadway  from  3  to  6  inches  lower  than  the  center; 
they  will  be  made  3  inches 
lower  than  the  center  in 
the  present  case.  The  top  of 
the  guard  angle  is  required 
by  B.  S.,  Art.  125,  to  be 
6  inches  above  the  floor;  this 
brings  it  3  inches  above  the 
top  of  the  floor  at  the  center.  fig.  4 

The  sidewalk  plank  rises  from  the  wheel-guard  toward  the 
railing  at  the  rate  of  i  inch  per  foot. 

6.  Spacing;  of  Stringers. — In  B.  S .,  Art.  93,  it  is 
specified  that,  for  bridges  carrying  a  street  railway  only, 
stringers  shall  be  spaced  6  feet  6  inches  center  to  center, 
and  that  for  other  bridges  they  shall  be  arranged  to  accom¬ 
modate  the  traffic.  In  the  present  case,  I  beams  will  be 
placed  3  feet  3  inches  on  each  side  of  the  center  line  of 
bridge  under  the  ties,  and  at  intervals  of  3  feet  for  the 
remainder  of  the  floor,  as  shown  in  Fig.  5.  An  I  beam  h  will 
also  be  placed  at  the  center  to  carry  any  loads  that  move 
along  the  center  of  the  car  track.  The  beam  a,  a ,  at  the  out¬ 
side  of  the  sidewalk,  under  the  railing,  is  frequently  made 
deeper  than  the  other  sidewalk  beams,  and  is  composed  of  a 
web  and  one  flange  angle  at  top  and  bottom;  it  is  then  called 
a  fascia  girder.  The  actual  location  of  the  fascia  girder 
depends  on  the  type  of  fence  railing  that  is  used,  and  on 
the  connection  of  the  posts  that  support  the  fence.  In  the 
present  case,  the  web  of  the  fascia  girder  will  be  assumed  to 
be  3  inches  outside  of  the  inner  edge  of  the  fence,  making 
the  web  3  feet  from  the  next  beam.  If  necessary,  this 
distance  can  be  changed  slightly,  when  detailing,  to  conform 
to  other  details. 


~0 


6  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


7' 


EH 


M- 


i/5 


7.  In  order  to  decrease  the  unsup¬ 
ported  length  of  the  upper  flange  of 
the  stringers,  so  that  a  higher  working 
stress  may  be  used,  cross-struts,  similar 
to  those  placed  between  the  I  beams  in 
the  highway  bridge  designed  in  Design 
of  Plate  Girders ,  Part  2,  will  be  placed 
between  the  stringers  at  the  center  of 
the  panels.  The  unsupported  length 
will  then  be  10  feet,  or  120  inches. 
The  weight  of  these  struts  is  so  small 
that  it  will  be  neglected  in  calculating 
moments  and  shears. 

8.  Design  of  Sidewalk  String¬ 
ers. — In  B.  S.,  Art.  98  (2),  the  live 
load  is  given  as  either  100  pounds  per 
square  foot  or  a  road  roller  weighing 
15  tons.  The  latter  need  not  be  con¬ 
sidered  on  the  sidewalk.  Since  the 

1  beams  are  3  feet  apart,  the  live  load 
due  to  the  uniform  load  is  300  pounds 
per  linear  foot  on  beam  b,  Fig.  5.  The 
floor  plank  2  inches  thick  weighs 

2  X  4.5  =  9  pounds  per  square  foot 
(see  B.  S .,  Art.  97),  and  the  part  sup¬ 
ported  by  beam  b  is  3  X  9  =  27  pounds 
per  linear  foot.  The  spiking  piece  will 
be  assumed  to  weigh  8  pounds  per 
linear  foot,  and  the  I  beam  20  pounds 
per  linear  foot.  The  total  load  sup¬ 
ported  by  the  beam  is,  therefore,  300 
+  27  +  8  +  20  =  355  pounds  per  linear 
foot,  and  the  maximum  bending  mo¬ 
ment,  since  the  floorbeams  are  20  feet 

,  ,  ,  .  355  X  20  X  20  .  0 

center  to  center,  is - - - X  12 

=  213,000  inch-pounds 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


7 


If  a  9-inch  21-pound  I  beam  is  used,  the  width  of  the  top 
flange  is,  by  Table  XIV,  4.33  inches;  and,  since  the  unsup¬ 
ported  length  is  120  inches,  the  allowable  working  stress, 
according  to  B.  S .,  Art.  103,  is 

120 


20,000  -  200  X 


4.33 


=  14,460  pounds  per  square  inch 


© 

© 

© 

*5 


-//'-O0- 


© 

© 

§ 


Fig.  6 


The  required  value  of  section  modulus  is  213,000  -r-  14,460 
=  14.73.  As  the  section  modulus  of  a  9-inch  21-pound 
I  beam  is  greater  than  this  (18.9, 

Table  XIV),  this  beam  will  be 
used.  An  8-inch  20.5-pound  beam 
could  have  been  used,  but,  as 
there  is  only  .5  pound  per  foot 
difference  between  the  two,  and  as  the  9-inch  beam  is  a 
standard  beam,  it  is  better  to  use  the  latter. 

The  live  load  supported  by  beam  c  is  somewhat  less  than 
that  supported  by  b,  as  part  of  the  width  between  beams  c 
and  d  is  occupied  by  the  width  of  the  truss.  It  is  not 
customary  to  make  allowance  for  this  in  the  design  of 
stringers,  however,  so  that  c  will  be  made  the  same  size  as  b. 

It  is  unnecessary 
to  design  the  fascia 
girder.  'The  thinnest 
allowable  web,  ~rs  inch 
(B.  X.,  Art.  112), 
and  the  smallest 
allowable  angles,  2\ 
in.  X  2i  in.  X  ijs  in.  {B.  S .,  Art.  113)  ,  will  usually  be  found 
to  give  sufficient  strength.  These  sections  will  be  used  in 
the  present  case. 


7.Z5 ' 


© 

© 

§ 


275‘ 


•/  * 


/O'-O' 


6.25' 


© 

© 

© 

*5 


</SS' 


-/oLo- 


-20-0*- 
Fig.  7 


9.  Design  of  Roadway  Stringers. — The  road  roller 
causes  a  greater  bending  moment  on  the  roadway  stringers 
than  the  uniform  load.  The  live  load  on  a  stringer  due  to 
the  road  roller,  according  to  B.  A.,  Art.  110  and  Art.  9§  (2) , 
is  represented  in  Fig.  6.  The  maximum  bending  moment 
on  the  beams  e  and  /,  Fig.  5,  is  found  to  occur  under  one  of 
the  loads  when  that  load  is  2.75  feet  from  the  center  of  the 


8 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


panel,  as  shown  in  Fig.  7,  and  is  315,400  inch-pounds. 
Since  the  I  beams  d ,  e ,  and  /,  Fig.  5,  are  3  feet  apart,  the 
dead  load  on  e  and  /  due  to  the  floor  plank  is  3  X  5  X  4.5 
=  67.5  pounds  per  linear  foot.  The  nailing  piece  will  be 
assumed  to  weigh  10  pounds,  and  the  I  beam  30  pounds, 
giving  a  total  dead  load  of  107.5  pounds  per  linear  foot. 
The  dead-load  moment  at  the  section  of  maximum  live-load 
moment,  2.75  feet  from  the  center,  is  59,600  inch-pounds, 
making  a  total  bending  moment  of  315,400  -j-  59,600 
=  375,000  inch-pounds.  If  a  10-inch  30-pound  I  beam  is 
used,  the  width  of  the  top  flange  is,  by  Table  XIV, 
4.8  inches,  and  the  allowable  intensity  of  working  stress, 
since  the  unsupported  length  of  flange  is  one-half  a  panel 
length,  or  120  inches  (Art.  7),  is 

190 

20,000  —  200  X  -  =  15,000  pounds  per  square  inch 

4.8 


© 

© 

© 


—  //-o- 


© 

© 

© 

•o 


The  required  section  modulus  is  375,000  15,000  =  25. 

As  the  section  modulus  of  a  10-inch  30-pound  I  beam  is 

greater  than  this 
(26.8,  Table  XIV), 
this  beam  will  be 
used. 

The  live  load  sup¬ 
ported  by  the  beam  d, 
Fig.  5,  is  somewhat 
less  than  the  live  load  supported  by  the  beams  e  and  /, 
but  it  is  customary  to  make  it  the  same  size  as  the  other 
roadway  beams,  and  so  a  10-inch  30-pound  I  beam  will  here 
be  used  for  each  of  the  beams  d ,  e ,  and  /. 


zo'-o"- 


Fig.  8 


10.  The  maximum  reaction  at  the  end  of  a  stringer  is 
found  to  occur,  for  the  loading  represented  in  Fig.  6,  when 
the  load  occupies  the  position  represented  in  Fig.  8.  The 
live-load  reaction  is  7,250  pounds,  and,  since  the  dead  load 
is  107.5  pounds  per  linear  foot,  the  dead-load  reaction  is 
1,075  pounds,  giving  a  total  reaction  of  8,325  pounds.  The 
connection  to  the  floorbeam  will  be  designed  in  Design  of  a 
Highway  Truss  Bridge ,  Part  2. 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


9 


11.  Design  of  Stringers  Under  Railway  Track. 
The  weight  of  the  street  car  is  given  in  B.  S.,  Art.  98  (4). 
One-half  of  it  will  be  assumed  to  go  to  each  rail;  the  rails 
will  be  taken  5  feet  center  to  center.  As  the  load  on  each 
axle  is  20,000  pounds,  the  load  on  each  wheel  will  be 
10,000  pounds.  The  two  wheels  on  each  axle  gre  located 
as  shown  in  Fig.  9,  with  respect  to  the  I  beams  g  and  h; 


ff  X  10,000,  or  7,692  pounds,  goes  to  each  of  the  beams 
marked^;  and  2  X  A  X  10,000,  or  4,615  pounds,  goes  to  the 
beam  h  at  the  center.  The  maximum  bending  moment  on  a 
stringer  occurs  when  there  are  two  wheels  in  a  panel,  one 
being  1.25  feet  from  the  center  and  the  other  3.75  feet  on  the 
other  side  of  the  center.  The  loading  for  beam  g  is  shown 
in  Fig.  10,  the  maximum  moment  being  706,700  inch-pounds, 
at  1.25  feet  from  the  center.  According  to  B.  S.f  Art.  99, 
there  must  be  added 
to  this,  to  provide  for 
impact  and  vibration, 

X  706,700  =  212,000 
inch-pounds,  givingfor 
the  total  live-load  mo¬ 
ment,  including  the 
allowance  for  impact  and  vibration,  918,700  inch-pounds. 
The  load  on  the  leeward  stringer  is  increased  on  account  of 
the  wind  pressure  on  the  side  of  the  car.  The  wind  pressure 
per  linear  foot,  as  given  in  B.  S.,  Art.  100,  is  250  pounds, 
applied  6  feet  above  the  top  of  the  rail.  The  length  of  the 
car  will  be  assumed  as  40  feet;  the  total  pressure,  therefore, 
is  40  X  250  =  10,000  pounds,  and  the  overturning  moment, 


6.75' 


Oi 


<’/J: 


3.75' 


•o 

o* 

05 

8 


6.25' 


-/o-o' 


-20-0' 


-/o'-o' 


Fig.  10 


10  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


77 


according  to  B.  S .,  Art.  100,  is  10,000  X  6  =  60,000  foot¬ 
pounds.  Since  the  rails  are  5  feet  center  to  center,  the 
increase  in  the  load  on  the  leeward  rail  is  60,000  -r-  5  —  12,000 
pounds,  one-quarter  of  which,  3,000  pounds,  goes  to  each 
of  the  four  wheels  on  the  leeward  side,  and  M  X  3,000 
=  2,308  pounds  goes  to  the  stringer  marked  g.  The  bend¬ 
ing  moment  due  to  this  increase  is  found  to  be  212,000  inch- 
pounds,  which  makes  the  total  bending  moment  1.25  feet 
from  the  center,  exclusive  of  dead  load,  1,130,700  inch-pounds. 


12.  The  dead-weight  of  the  ties,  nailing  pieces,  rails,  and 
floor,  including  one-half  the  width  of  floor  between  the 
beams  g  and  /  (see  Fig.  5),  will  be  assumed  to  be  equally 
distributed  among  the  three  beams  g,  h,  and  g}  as  shown  to 
larger  scale  than  before  in  Fig.  11.  The  ties,  according  to 


Fig.  11 


B.  S .,  Art.  121,  will  be  6  in.  X  6  in.  X  8  ft.,  spaced  15  inches 
center  to  center.  The  weight  of  each  tie  is  108  pounds, 
corresponding  to  86.4  pounds  per  linear  foot  of  track  (since 
the  ties  are  spaced  1.25  feet  center  to  center).  The  com¬ 
bined  weight  of  the  five  spiking  pieces  will  be  assumed  to  be 
25  pounds  per  linear  foot,  and  of  the  two  rails,  40  pounds 
per  linear  foot.  Since  the  floor  is  5  inches  thick,  and  a  width 
of  9  feet  6  inches  is  supported  by  the  three  beams,  the  weight 
of  this  portion  is  5  X  4.5  X  9.5  =  213.75  pounds  per  linear 
foot,  which  makes  the  total  dead-weight  supported  by  the 
three  beams,  not  including  their  own  weight, 

86.4  -f  25  +  40  +  213.75  =  365.15  pounds  per  linear  foot, 
and  that  supported  by  each  beam  one-third  of  this,  or,  say, 
125  pounds  per  linear  foot. 


§  77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


11 


13.  The  weight  of  the  beam  g  will  be  assumed  to  be 
55  pounds  per  linear  foot,  making  the  total  dead  load  on 
this  beam  125  -f  55  —  180  pounds  per  linear  foot.  The 
dead-load  moment  at  the  section  where  the  live-load  moment 
is  greatest,  that  is,  at  1.25  feet  from  the  center  of  the  panel, 
is  106,300  inch-pounds.  The  total  bending  moment  is,  there¬ 
fore,  1,130,700  +  106,300  —  1,237,000  inch-pounds.  If  an 
18-inch  55-pound  beam  is  used,  as  the  width  of  the  flange 
(Table  XIV)  is  6  inches  and  the  unsupported  length  of  the 

top  flange  is  120  inches,  the  ratio  —  will  be  20.  Accord¬ 
ed 

ing  to  B.  S.,  Art.  103,  the  allowable  working  stress  is 
16,000  pounds  per  square  inch.  Then,  the  required  value 
of  the  section  modulus  is  1,237,000  16,000  =  77.3.  In 

Table  XIV,  the  section  modulus  of  an  18-inch  55-pouncl 
beam  is  found  to  be  88.4,  which  is  greater  than  the  required 
value.  This  beam  will  be  used  for  beams  g. 


Oi 

to 


S-0‘ 


*© 

to 

s 


20-0"- 


Fig.  12 


14.  The  amount  of  load  that  goes  to  beam  g  from  each 
wheel  was  found,  in 
Art.  11,  to  be  7,692 
pounds.  The  maxi¬ 
mum  live-load  shear 
is  found  to  occur  at 
the  end,  when  two 
loads  are  in  a  panel, 
as  represented  in  Fig.  12,  and  is  equal  to  13,460  pounds. 
The  allowance  for  impact  and  vibration  is  Ay  X  13,460 
=  3  X  1,346  =  4,040  pounds;  and  the  allowance  for  the 
overturning  effect  of  the  wind  is  2,308  pounds.  Since  the 
dead  load  is  180  pounds  per  linear  foot,  the  dead-load  shear 
at  the  end  is  equal  to 

180  X  20  ,  on„ 

- tt—  =  1,800  pounds, 


making  the  total  shear  at  the  end 

13,460  +  2,308  +  4,040  +  1,800  =  21,610  pounds 
The  connection  to  the  floorbeam  will  be  designed  in 
Design  of  a  Highway  Truss  Bridge ,  Part  2. 

135-12 


I 


12  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 

15.  Design  of  Center  Stringer. — The  amount  of  load 
that  goes  to  the  beam  h ,  Fig.  5,  from  each  axle  was  found 
in  Art.  11  to  be  4,615  pounds.  The  maximum  bending 
moment  is  found  in  the  same  way  as  for  beam  g  at  a  section 
1.25  feet  from  the  center,  and  is  424,000  inch-pounds. 
The  allowance  for  impact  and  vibration  is  -ft  X  424,000 
=  127,200  inch-pounds.  It  is  unnecessary  to  allow  for  any 
increase  due  to  the  wind:  the  overturning  tendency  of  the 
wind  increases  the  load  on  the  leeward  rail,  but  at  the  same 
time  decreases  the  load  on  the  windward  rail  by  an  equal 
amount,  and,  since  beam  h  gets  its  load  from  both  rails,  the 
amount  that  goes  to  it  is  neither  increased  nor  diminished. 

The  dead  load  supported  by  the  beam  h  has  been  found 
to  be  125  pounds  per  linear  foot;  the  weight  of  the  beam 
will  be  assumed  to  be  40  pounds  per  linear  foot,  making  the 
total  dead  load  165  pounds  per  linear  foot.  The  dead-load 
moment  at  the  section  where  the  live-load  moment  is  greatest, 
that  is,  at  1.25  feet  from  the  center  of  the  panel,  is  97,500  inch- 
pounds.  The  total  bending  moment  is,  therefore, 

424,000  +  127,200  +  97,500  -  648,700  inch-pounds 

If  a  12-inch  40-pound  beam  is  used,  as  the  width  of  flange 
(Table  XIV)  is  5.25  inches,  and  the  unsupported  length  of 
the  top  flange  is  120  inches,  the  allowable  intensity  of  bend¬ 
ing  stress  ( B .  S.,  Art.  103)  is 

190 

20,000  —  200  X  — -  —  15,430  pounds  per  square  inch 

o.zo 

Then,  the  required  section  modulus  is  648,700  -r-  15,430 
=  42.04.  In  Table  XIV,  the  section  modulus  of  a  12-inch 
40-pound  I  beam  is  found  to  be  44.8,  which  is  greater  than 
the  required  value,  and  this  is  the  lightest  beam  that  can  be 
used.  A  12-inch  40-pound  I  beam  will  be  chosen  for  beam  h. 

16.  The  maximum  live-load  shear  is  found  in  the  same 
way  as  for  beam  g  to  be  8,080  pounds.  The  allowance  for 
impact  and  vibration  is  ft  X  8,080  =  2,420  pounds.  Since 
the  dead  load  is  165  pounds  per  linear  foot,  the  dead-load 
shear  is  1,650  pounds,  making  the  total  shear  at  the  end 

8,080  +  2,420  +  1,650  =  12,150  pounds 


§  77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  13 

INTERMEDIATE  FLOORBEAMS  AND  BRACKETS 

17.  Eengtli  and  Depth. — The  roadway  is  supported 
by  floorbeams  attached  to  the  trusses  at  the  panel  points. 
The  sidewalks  are  supported  on  brackets  outside  of  the 
trusses.  These  brackets  are  sometimes  continuations  of 
the  floorbeams  and  sometimes  independent;  in  the  latter 
case,  they  are  riveted  to  the  vertical  posts  of  the  trusses  on 
the  side  opposite  that  to  which  the  floorbeam  is  riveted,  and 
the  flanges  of  the  brackets  are  connected  with  the  flanges 
of  the  floorbeams  in  such  a  way  that  the  brackets  and  floor- 
beam  act  as  a  single  beam.  The  method  of  connection  that 
will  be  employed  in  the  present  case  will  be  discussed  in 
Design  of  a  Highway  Truss  Bridge ,  Part  2. 

The  total  length  of  the  beam,  including  the  brackets,  is 
the  distance  between  the  fascia  girders;  in  the  present  case, 
this  distance  is  42  feet  6  inches,  as  shown  in  Fig.  5.  The 
distance  between  the  supports  is  equal  to  the  distance  center 
to  center  of  the  trusses,  or  28  feet.  The  depth  of  floorbeam 
will  be  made  equal  to  one-eighth  the  distance  between 
trusses,  or  28  -f-  8  =  3.5  feet.  The  load  is  transmitted  to 
the  beam  by  the  stringers;  their  location  a ,  b,  c,  etc.,  along 
the  beam,  and  the  location  of  the  trusses  A  and  B  are  shown 
in  Fig.  13. 

18.  Dead  Eoad. — The  railing  ordinarily  weighs  about 
40  pounds  per  linear  foot,  and  the  fascia  girder  about 
35  pounds  per  linear  foot;  in  the  present  case,  the  two 
together  will  be  assumed  to  weigh  75  pounds  per  linear  foot. 
Since  the  distance  center  to  center  of  the  floorbeams  is 
20  feet,  the  amount  of  load  that  goes  to  the  end  of  each 
beam  or  bracket  is  20  X  75  =  1,500  pounds  ( a ,  Fig.  13). 
The  dead  load  on  each  sidewalk  stringer  was  found  in 
Art.  8  to  be  55  pounds  per  linear  foot;  therefore,  the  load 
that  comes  to  the  floorbeam  at  each  sidewalk  stringer  is 
20  X  55  =  1,100  pounds  ( b  and  c,  Fig.  13).  The  dead  load 
on  each  roadway  stringer  was  found  in  Art.  9  to  be 
107.5  pounds  per  linear  foot;  therefore,  the  load  that  comes 


14 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §  77 


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to  the  floorbeam  at  each  roadway 
stringer  is  20  X  107.5  =  2,150 
pounds  (d,  e ,  and  /,  Fig.  13). 
The  dead  load  on  each  of  the 
stringers  g  under  the  railway 
track  was  found  in  Art.  13  to  be 
180  pounds  per  linear  foot;  there¬ 
fore,  the  load  that  comes  to  the 
floorbeam  at  each  of  these  string¬ 
ers  is  20  X  180  =  3,600  pounds 
(g,  Fig.  13).  The  dead  load  on 
the  center  stringer  was  found  in 
Art.  15  to  be  165  pounds  per 
linear  foot;  therefore,,  the  load 
that  comes  on  the  floorbeam  at 
the  center  is  20  X  165  =  3,300 
pounds  (/z,  Fig.  13). 

19.  No  rule  or  formula  can  be 
given  by  means  of  which  the 
weight  of  brackets  and  floorbeams 
can  be  calculated.  In  every  case 
it  is  necessary  to  estimate  first, 
and  then  correct  the  estimate. 
An  experienced  designer  will  esti¬ 
mate  closely  the  first  time.  In  the 
present  case,  the  weight  of  each 
bracket  will  be  assumed  to  be 
75  pounds  per  linear  foot,  and 
the  weight  of  the  floorbeam  125 
pounds  per  linear  foot.  As  the 
loading  is  symmetrical  about  the 
two  supports  A  and  B,i  Fig.  13, 
each  reaction  is  equal  to  one-half 
the  sum  of  all  the  loads  on  the 
beam  and  brackets,  together  with 
one-half  the  weight  of  beam  and 
bracket,  or  17,694  pounds.  Fig.  13 


§  77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


15 


shows  the  total  dead  load  on  the  floorbeam  and  the  dead¬ 
load  reactions. 

20.  Dead-Toad  Shears. — As  a  rule,  it  is  sufficient  to 
find  the  shears  on  the  bracket  and  on  the  floorbeam  at  sec¬ 
tions  close  to  the  trusses.  Considering  the  left  truss  A, 
Fig.  13,  the  shear  on  the  bracket  just  to  the  left  of  A  is 
negative  and  equal  to  4,240  pounds,  and  that  on  the  floorbeam 
just  to  the  right  of  A  is  positive  and  equal  to  13,450  pounds. 
If  it  is  found  necessary  in  the  design  of  the  web  and  the 
computation  of  rivet  pitch  to  know  the  shears  at  other  sec¬ 
tions,  they  can  be  computed  later  at  sections  between  the 
stringer  connections. 

21.  Dead-Toad  Moments. — As  a  rule,  it  is  sufficient 
to  find  the  moment  on  the  bracket  where  it  connects  to  the 
truss,  and  on  the  floorbeam  at  the  center  of  the  bridge. 
The  moment  on  the  bracket  where  it  connects  to  the  truss  is 
negative,  and  equal  to  226,800  inch-pounds.  The  moment 
on  the  floorbeam  at  the  center  is  positive,  and  equal  to 
1,029,500  inch-pounds.  If  it  is  found  necessary  in  the  design 
of  the  flanges  to  know  the  moments  at  other  sections,  they 
can  be  computed  later  at  the  sections  where  the  stringers 
connect  with  the  floorbeams. 

22.  Tive  Toad. — The  uniform  live  load  is  100  pounds 
per  square  foot  [ B .  S.,  Art.  98  (2)].  According  to  B.  S ., 

Ci  Oi  Ci 


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Fig.  14 

Art.  98  (5),  the  uniform  load  is  to  be  taken  as  covering  the 
entire  floor  except  a  width  of  10  feet  for  the  car  track.  In 
the  design  of  floorbeams  in  a  bridge  that  carries  a  street-car 


16  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


77 


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track,  it  is  customary  to  consider  only  the  uniform  load 

and  the  weight  of  a  street  car,  and 
to  ignore  the  effect  of  the  road 
roller,  as  it  will  probably  never  cross 
the  bridge  at  the  same  time  as  a 
street  car.  The  portion  of  the  width 
occupied  by  the  truss  and  wheel- 
guard — in  this  case,  2  feet  6  inches 
at  each  side — is  not  assumed  to  sup¬ 
port  any  live  load. 

The  maximum  load  that  comes 
to  a  floorbeam  from  the  stringers 
marked  g,  Fig.  5,  occurs  when  the 
loads  in  the  panel  ahead  of  and  in 
the  panel  behind  the  floorbeam  are 
located  as  represented  in  Fig.  14. 
The  portion  of  the  weight  on  one 
wheel  that  goes  to  a  beam  g  has 
been  found  to  be  .7,692  pounds;  then, 
the  load  on  the  floorbeam  is  15,384 
pounds.  In  like  manner,  the  load  on 
the  floorbeam  at  the  center  stringer 
is  found  to  be  9,230  pounds.  As 
these  loads  come  from  the  car,  the 
stresses  due  to  them  must  be 
increased  to  allow  for  impact  and 
vibration;  in  the  present  case,  the 
work  will  be  much  simplified  and 
the  results  will  be  the  same  if  the 
foregoing  floorbeam  loads  are 
increased  by  the  proper  amount. 
The  load,  including  impact  and  vibra¬ 
tion  on  the  floorbeam  at  the  center 
stringer,  is,  then,  9,230  +  Ao  X  9,230 
=  12,000  pounds,  and  at  each  of 
the  stringers  marked  g,  Fig.  5,‘ 
15,384  +  Ao  X  15,384  =  20,000 


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77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  17 


the  leeward  stringer  is  not  considered  in  the  design  of  the 
floorbeam. 

23.  The  clear  width  of  each  sidewalk  is  6  feet.  Since 
the  panels  are  20  feet  in  length,  the  uniform  load  on  each 
bracket  is  20  X  100  =  2,000  pounds  per  linear  foot  for  a 
distance  of  6  feet,  and  extends  to  within  1  foot  of  the  center 
line  of  the  truss,  as  represented  in  Fig.  15. 

The  clear  width  of  roadway  between  wheel-guards  is  25  feet. 
Allowing  10  feet  for  the  load  on  the  car  track  leaves  a 
width  of  15  feet,  or  7.5  feet  on  each  side  of  the  track  that  is 
covered  by  the  uniform  load  of  2,000  pounds  per  linear  foot. 
Since  the  edge  of  the  wheel-guard  toward  the  roadway  is 
1  foot  6  inches  from  the  center  line  of  the  truss,  the  uniform 
load  will  extend  to  within  1  foot  6  inches  of  the  center  line, 
as  shown  in  Fig.  15. 


24.  It  is  unnecessary  to  compute  the  amount  of  load 
that  comes  to  the  floorbeam  at  each  sidewalk  and  roadway 
stringer.  If  the  moments  and  shears  are  found  for  the  load¬ 
ing  shown  in  Fig.  15,  the  results  will  be  close  enough  to  the 
actual  values  for  all  practical  purposes.  Since  the  loading 


f-6" 


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28 -0‘ 


Fig.  16 


is  symmetrical,  the  reactions  at  A  and  B  are  each  equal  to 
one-half  the  total  load  on  the  beam,  or,  in  this  case, 
53,000  pounds. 


25.  Dive-Load  Shears. — The  live-load  shear  on  the 
bracket  just  to  the  left  of  A  is  negative  and  equal  to 
12,000  pounds.  The  live-load  shear  on  the  floorbeam  just 
to  the  right  of  A  is  positive  and  equal  to  41,000  pounds. 


IS 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §  77 

26.  Dive-Load  Moments. — The  live-load  moment  on 
the  bracket  is  negative  and  greatest  at  A ;  it  is  equal  to 
576,000  inch-pounds.  The  live-load  moment  on  the  floor- 
beam  is  greatest  at  the  center,  when  there  is  no  live  load  on 
the  overhanging  or  sidewalk  brackets,  and  there  is  a  full 
load  on  the  floorbeam,  as  shown  in  Fig.  16;  it  is  positive  and 
equal  to  4,533,000  inch-pounds. 

27.  Design  of  Floorbeam  Web. — The  total  shear  on 
the  floorbeam  at  the  end  is  13,450  +  41,000  —  54,450  pounds. 
It  was  decided  in  Art.  17  that  a  web  42  inches  wide  would 
be  employed.  It  is  good  practice  in  this  type  of  floor  to  use 
a  thickness  of  web  that  will  require  no  stiffeners  between 
the  stringer  connections.  Then,  the  smallest  allowable 
unsupported  distance  is  the  clear  distance  between  the 
flange  angles,  probably  about  34  inches  in  this  case,  or  the 
clear  distance  between  stringer  connections,  which  is  about 
the  same.  The  connection  of  stringer  d,  Fig.  5,  to  the  floor- 
beam  is  so  close  to  the  end  that  no  stiffeners  will  be  required 
between  the  end  of  the  floorbeam  and  this  connection;  hence, 
the  intensity  of  shearing  stress  at  the  end  of  the  floorbeam 
need  not  be  computed.  The  total  shear  on  the  floorbeam  in 
the  next  space,  that  is,  between  stringers  d  and  must  now 
be  found,  so  that  the  allowable  unsupported  distance  can  be 
determined.  The  shear  is  practically  constant  from  d  to  <?, 
and  if  it  is  found  half  way  between  them,  the  result  will  be 
close  enough.  This  shear  is  found  by  deducting  from  the 
end  shear  the  sum  of  all  the  loads  between  the  end  and  the 
point  at  which  the  shear  is  desired.  The  shear  is  as  follows: 
54,450  -  (3.25  X  125  +  2,150  +  1.75  X  2,000)  -  48,390pounds. 

Using  a  web  f  inch  thick,  the  area  of  cross-section  is 
15.75  square  inches;  the  intensity  of  shear  is  48,390  -r-  15.75 
=  3,072  pounds  per  square  inch,  and  the  allowable  unsup¬ 
ported  distance  (Table  XXXVI)  is  35  inches.  As  this  is 
greater  than  34  inches,  a  42"  X  i"  web  will  be  used,  and 
no  stiffeners  will  be  provided  except  at  the  stringer  con¬ 
nections,  which  are  points  of  local  concentrated  loading 
(B.S.,  Art.  128). 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  19 


28.  Design  of  Floorbeam  Flanges. — The  required 
area  of  flange  will  be  found  from  the  following  formula, 
given  in  Design  of  Plate  Girders ,  Part  1: 

^  _  M  t  h 
s  hg  8 

In  the  present  case,  th  is  15.75  square  inches,  M  is 
1,029,500  +  4,533,000  =  5,562,500  inch-pounds,  s  is  16,000 
pounds  per  square  inch  ( B .  S.,  Art.  103),  and  he  is  not 
known,  but  will  be  assumed  for  trial  equal  to  the  depth  of 
web,  or  42  inches.  Then, 

a  5,562,500  15.75  q  no  i  0^7  o  01  •  1 

A  =  „  ’ — — - - —  =  8.28  —  1.97  =  6.31  square  inches 

16,000  X  42  8 


For  the  top  flange,  two  4"  X  4//  X  angles  will  be  tried. 
The  gross  area  is  2  X  3.75  =  7.5  square  inches,  and  the 
center  of  gravity  is  1.18  inches  from  the  backs  of  the  angles 
(Table  IX) .  For  the  bottom  flange,  two  4"  X  4"  X  iV7  angles 
will  be  tried.  The  gross  area  of  one  angle  (Table  IX)  is 
4.18  square  inches;  the  area  to  be  deducted  for  one  f-inch 
rivet  (Table  XXVII)  is  .49  square  inch.  Then,  the  net  area 
of  one  angle  is  4.18  —  .49  =  3.69  square  inches,  and  that  of 
two  angles  is  7.38  square  inches.  The  center  of  gravity  of 
the  angles  is  1.21  inches  from  the  backs  of  the  angles.  The 
distance  center  to  center  of  gravity  of  the  flanges  is,  there¬ 
fore,  42.25  —  1.18  —  1.21  =  39.86  inches.  Using  this  value 

5,562,500  15.75 


for  hg  gives  A  = 


16,000  X  39.86 


8 


8.72  -  1.97 


=  6.75  square  inches.  ,  * 

As  the  flanges  that  have  been  tried  have  the  required  area, 
they  will  be  used,  that  is,  two  4"  X  4"  X  i77  angles  for  the 
top  flange  and  two  4"  X  4"  X  iV7  angles  for  the  bottom  flange. 
As  there  are  no  flange  plates,  and  the  angles  are  continued 
the  full  length  of  the  floorbeam,  it  is  not  necessary  to  draw 
a  curve  of  the  flange  areas  nor  to  calculate  the  moment  at 
any  other  section. 


29.  Flange  Rivets  in  Floorbeams. — The  pitch  of  rivets 

Jl 

in  the  flanges  will  be  found  by  the  formula  p  =  --—4  (see 


20 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §  77 


Design  of  Plate  Girders,  Part  1).  In  Table  XII,  the  gauge 
line  of  an  angle  4  inches  wide  is  shown  to  be  2i  inches  from 
the  back  of  the  angle.  Since  the  flange  angles  are  42.25  inches 
back  to  back,  the  distance 

hr  =  42.25  -  2.25  -  2.25  =  37.75  inches 

The  flange  rivets  are  usually  f  inch  in  diameter  and  shop 
driven;  according  to  B.  S.,  Art.  103,  the  allowable  working 
stresses  are  11,000  pounds  per  square  inch  in  shearing  and 
22,000  pounds  per  square  inch  in  bearing.  The  rivets  are  in 
double  shear  and  in  bearing  on  the  f-inch  web-plate.  Con¬ 
sulting  Table  XL,  the  bearing  value  is  found  to  be  the 
smaller,  the  value  being  6,190  pounds.  At  the  end  of 
the  floorbeam,  where  the  beam  connects  to  the  truss, 
V  54,450  pounds;  therefore, 

p  —  6490  X  37.75  _  4  29  inches  at  end  of  floorbeam 
54,450 

Half  way  between  d  and  e,  the  shear  was  found  to  be 
48,390  pounds;  therefore, 

P  —  ~  —  4-83  inches  from  d  to  e ,  Fig.  13 

y  48,390  s 

Half  way  between  e  and  /,  the  shear  is  equal  to 

54,450  -  (6.25  X  125  +  2  X  2,150  +  4.75  X  2,000) 

=  39,870  pounds; 

therefore, 

P  —  — "  =  5-86  inches  from  e  to  /,  Fig.  13 

39,870 

Beyond  /,  the  rivet  pitch  comes  out  greater  than  6  inches, 
and  it  is  unnecessary  to  calculate  it,  as  the  greatest  allowable 
pitch  is  6  inches  ( B .  S.,  Arts.  115  and  130).  Consequently, 
a  pitch  of  6  inches  will  be  used  for  the  remainder  of  the  flange. 

30.  Design  of  Sidewalk  Brackets. — It  is  customary 
to  make  the  sidewalk  bracket  the  same  depth  as  the  floor- 
beam  where  it  connects  with  the  truss,  and  to  make  it  about 
1  foot  deep  at  the  outside  edge  of  the  sidewalk,  as  shown  in 
Fig.  17.  The  web  shear,  rivet  pitch,  and  flange  area  should 
be  computed  at  the  point  or  section  of  maximum  bending 
moment.  This  occurs  where  the  bracket  connects  with  the 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  21 


truss,  which  is  for  convenience  assumed  to  be  the  center  of 
the  truss.  As  a  rule,  if  the  thinnest  allowable  web  is  used, 
and  each  flange  is  made  of  two  of  the  smallest  allowable 
angles — in  this  case,  2|  in.  X  2i  in.  X  A  in.  ( B .  S.,  Art.  113) 
— the  bracket  will  have  sufficient  strength. 

The  maximum  total  shear  on  the  bracket  is  the  sum  of  the 
dead  shear,  4,240  pounds,  as  found  in  Art.  20,  and  the  live 
shear,  12,000  pounds,  as  found  in  Art.  25;  its  value  is,  there¬ 
fore,  16,240  pounds.  If  a  A-inch  web  42  inches  deep  at  the 
truss  is  used,  then,  as  the  area  of  the  web  is  13.125  square 
inches,  the  intensity  of  shearing  stress  is  16,240  -*•  13.125 
=  1,240  pounds  per  square  inch.  Consulting  Table  XXXVI, 
the  allowable  unsupported  distance  is  found  to  be  about 
50  inches.  This  web  can  therefore  be  used,  and  no  stiff¬ 
eners  will  be  required 
except  at  stringer  con¬ 
nections  ( B .  S.y  Art. 

128). 

The  maximum  bend-  A 
ing  moment  is  226,800 
+  576,000  -  802,800 
inch-pounds.  The 
area  of  flange  is  cal¬ 
culated  by  the  formula 


T“ 

vl 

i 


Roadway 


F/oor  Beam 


Fig.  17 


A  —  (see  Design  of  Plate  Girders ,  Part  1),  as  it  is  not  cus- 
s  hs 

tomary  to  consider  the  effect  of  the  web  in  a  sidewalk 
bracket.  The  trial  value  for  hg,  42  inches,  will  first  be  used. 
This  gives,  since  M  =  802,800  foot-pounds  and  s  —  16,000 
pounds  per  square  inch, 

A  —  — 8Q2’8Q0 —  =  1.19  square  inches 
16,000  X  42 

The  gross  area  of  two  X  X  iV7  angles  is  2  X  1.46 
=  2.92  square  inches.  Allowing  one  hole  for  a  f-inch  rivet 
in  each  angle,  the  net  area  is  2.92  —  2  X  .273  =  2.37  square 
inches.  As  both  of  these  are  much  greater  than  the  trial 
value  of  the  required  area,  it  is  unnecessary  to  compute  the 
true  values  of  he  and  A. 


22  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §  77 


31.  The  required  pitch  of  rivets  is  found  by  the  formula 

_  Khr  The  rjvets  are  jn  double  shear  and  in  bearing  on 
1  V 

a  web  i~e  inch  thick.  Consulting  Table  XL,  the  bearing  value 
is  found  to  be  the  smaller,  and  is  5,160  pounds.  The  shear  V 
has  been  found  to  be  16,240  pounds.  The  distance  back 
to  back  of  angles  at  the  deepest  portion  of  the  bracket  is 
42.25  inches.  Consulting  Table  XII,  the  gauge  line  of  a 
22-inch  angle  is  found  to  be  If  inches  from  the  back  of 
the  angle,  giving  the  value  of  hr  —  42.25  —  1.375  —  1.375 
=  39.5  inches.  Then, 

=  5,160  x  39J>  =  12  g  •  h 
16,240 

As  this  is  greater  than  the  maximum  allowable  pitch 
[6  inches  ( B .  A.,  Art.  130)],  the  latter  will  be  used  through¬ 
out  the  flanges.  _ 

END  FLOORBEAM  AND  BRACKET 

32.  Length  and  Depth. — It  is  generally  advisable  to 
leave  the  design  of  the  end  floorbeam  until  after  the  design 
of  the  trusses,  as  the  depth  of  the  floorbeam  must  be  made 
to  conform  to  details  that  depend  on  the  design  of  the  truss. 
For  convenience,  however,  the  end  floorbeam  will  now  be 
designed,  the  depth  being  taken  as  34f  inches,  as  found  in  a 
subsequent  article.  The  length  and  distances  along  the  beam 
and  bracket  are  the  same,  as  for  the  other  floorbeams,  as  found 
in  Art.  6. 

33.  Dead  Load. — The  portion  of  the  dead  load  that  goes 
to  the  end  floorbeam  from  the  stringers  is  one-half  that 
shown  in  Fig.  13;  the  weight  of  bracket  will  be  assumed  to 
be  75  pounds  per  linear  foot,  and  of  the  floorbeam  100  pounds 
per  linear  foot.  The  dead  loads  are  shown  in  Fig.  18. 

34.  Dead-Load  Shears  and  Moments. — The  shear  on 
the  floorbeam  at  its  connection  to  the  truss  is  7,250  pounds, 
and  the  moment  at  the  center  of  the  floorbeam  is  547,000  inch- 
pounds.  It  is  not  necessary  to  compute  the  shear  and  bending 
moment  on  the  bracket,  which  will  have  sufficient  strength  if 


S  77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


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24  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


77 


the  web  is  made  inch  thick,  and  each  flange  is  composed 
of  two  X  2i"  X  iV'  angles. 

35.  Dive  Load. — The  live  load  on  the  end  floorbeam, 
due  to  the  uniform  load  on  the  floor,  is  one-half  that  shown 
in  Fig.  16,  or  1,000  pounds  per  linear  foot.  The  live  loads 
at  the  stringers  g  and  h  are  more  than  one-half  those  shown 
in  Fig.  16,  and  are  greatest  when  the  wheels  are  in  the  posi¬ 
tion  shown  in  Fig.  12.  The  loads  at  g  and  h ,  including  the 
allowance  for  impact  and  vibration,  are,  respectively,  17,500 
and  10,500  pounds.  The  live  loads  on  the  end  floorbeam  are 
shown  in  Fig.  19. 

36.  Dive-Doad  Shears  and  Moments. — The  live-load 
shear  on  the  end  floorbeam  at  its  connection  with  the  truss 
is  30,250  pounds,  and  the  bending  moment  at  the  center  of 
the  floorbeam  (when  there  is  no  live  load  on  the  brackets)  is 
3,612,000  inch-pounds. 


37.  Design  of  Web. — The  total  shear  on  the  floorbeam 
is  7,250  +  30,250  =  37,500  pounds.  If  a  iVinch  web  is 
used,  the  area  of  cross-section  is  34  X  tY  =  10.625  square 
inches,  and  the  intensity  of  shearing  stress  is  37,500  -5-  10.625 
=  3,530  pounds  per  square  inch.  Consulting  Table  XXXVI, 
it  is  seen  that  the  allowable  unsupported  distance  of  the  web 
is  27  inches.  If  4-inch  angles  are  used  in  the  .  flanges,  the 
clear  distance  between  them  will  be  26  inches,  and  no 
stiffeners  will  be  required. 


38.  Design  of  Flanges. — The  required  area  of 

M  th 


flange  will  be  found  from  the  formula  A  = 


5  he 


8 


the 

In 


the  present  case,  th  is  10.625  square  inches,  M  is  547,000 
-h  3,612,000  =  4,159,000  inch-pounds,  s  is  16,000  pounds  per 
square  inch,  and  hs  is  not  known.  In  the  design  of  the 
intermediate  floorbeams,  it  was  found  that  the  value  of  hg 
was  1.18  1.21  =  2.39  inches  less  than  the  distance  back  to 

back  of  flange  angles.  For  trial,  it  will  be  assumed  that  he 
in  the  end  floorbeam  is  the  same  amount  less  than  the 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  25 


distance  back  to  back  of  flange  angles,  or  34.25  —  2.39 
=  31.86  inches.  Then, 

4,159,000  10.625 


A  = 


8.16  -  1.33 


16,000  X  31.86  8 

=  6.83  square  inches 

For  the  top  flange,  two  4"  X  4"  X  i"  angles  will  be  tried. 
The  gross  area  is  2  X  3.75  =  7.50  square  inches,  and  the  center 
of  gravity  is  1.18  inches  from  the  back  of  the  angles.  For 
the  bottom  flange,  two  4"  X  4"  X  iV/  angles  will  be  tried.  The 
net  area  of  each  angle,  if  one  f-inch  rivet  hole  is  deducted, 
is  4.18  —  .49  =  3.69  square  inches,  and  of  two  angles, 
7.38  square  inches.  The  center  of  gravity  is  1.21  inches 
from  the  back  of  the  angles.  The  distance  hg  between  the 
centers  of  gravity  of  the  flanges  is,  then,  34.25  —  1.18  —  1.21 
=  31.86  inches,  as  was  assumed.  The  trial  value  of  the 
required  area  found  is,  therefore,  the  actual  flange  area 
required. 

39.  Flange  Rivets. — The  pitch  of  rivets  will  be  found 

Khr 


by  the  formula  p  = 


V 


In  the  present  case,  the  value  of 


Fis  7,250  +  30,250  =  37,500  pounds,  and  hr  =  34.25  -  4.5 
=  29.75  inches.  The  rivets  are  in  double  shear  and  in  bear¬ 
ing  on  the  web  ve  inch  thick;  the  latter  value  is  the  smaller, 
and  is  5,160  pounds.  Then, 

.  5,160  X  29.75  .  nQ  .  . 

P  =  ~  37.500  =  4'°9  lnCh6S 

This  is  very  nearly  the  same  as  the  pitch  at  the  end  of  the 
intermediate  floorbeam;  hence,  the  same  rivet  spacing  will 
be  used  for  both. 

40.  Sidewalk  Bracket. — There  is  no  need  to  design 
the  sidewalk  bracket;  the  web  will  be  made  34  inches  deep 
at  the  truss  and  ins  inch  thick,  and  two  2|//  X  2i"  X  i V' 
angles  will  be  used  in  each  flange. 


26  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


DESIGN  OF  MAIN  MEMBERS  AND 
LATERAL  SYSTEM 


STRESSES  IN  MAIN  MEMBERS 

41.  Live-L  oad  Stresses. — According  to  A*.  S.t 
Art.  98  (2),  the  uniform  load  on  the  floor  to.  be  used  in  the 
design  of  the  trusses  is  80  pounds  per  square  foot  for 
bridges  100  feet  in  length,  and  60  pounds  per  square  foot 
for  bridges  200  feet  in  length.  The  uniform  load  for  the 
bridge  under  consideration  (160  feet  in  length)  is,  therefore, 
68  pounds  per  square  foot.  The  total  load  on  the  two  side¬ 
walks  is  2  X  6  X  68  =  816  pounds  per  linear  foot,  and  on 
the  roadway,  exclusive  of  a  width  of  10  feet  for  the  car 
track  [ B .  A.,  Art.  98  (5)],  is  2  X  7.5  X  68  =  1,020  pounds 
per  linear  foot,  making  the  total  live  uniform  load  on  the 
floor  1,020  +  816  =  1,836  pounds  per  linear  foot.  The  panel 
loads  are  each 

1,836  X  20  =  18  860  pounds> 

2 

and  the  reaction  for  each  truss  when  fully  loaded  (neglecting 
the  half-panel  loads  at  each  end)  is 

18,360  x7  =  64,260  pounds 
z 

The  stresses  caused  in  the  chord  members  by  this  portion 
of  the  live  load  are  determined  as  explained  in  Stresses  in 
Bridge  Trusses ,  Part  2,  and  are  as  follows  (see  Fig.  20): 


Member  Stress,  in  Pounds 


cib,b  c 

47,600  (tension) 

c  d 

81,600  (tension) 

de 

102,000  (tension) 

BC 

81,600  (compression) 

CD 

102,000  (compression) 

DE 

108,800  (compression) 

§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  27 


The  shears  in  the  panels  due  to  this  portion  of  the  load 
are  as  follows: 


Panel 

a  b 
be 
c  d 
de 


Shear, 
in  Pounds 

64,260 

48,195 

34,425 

22,950 


Panel 

e  d' 
d'e' 
c'  bf 
b’  a! 


Shear, 
in  Pounds 

13,770 

6,885 

2,295 

0 


42.  According  to  B.  S .,  Art.  98  (4),  the  load  on  the  car 
track  for  a  span  of  160  feet  must  be  taken  as  1,345  pounds 
per  linear  foot  for  the  computation  of  the  chord  stresses. 
This  gives  a  panel  load  for  each  truss  of  13,450  pounds,  and 
each  reaction  for  a  full  load  (neglecting  the  half-panel  loads 
at  the  ends)  is 

13,450  X  7  A  rj  A 

— 5 —  =  47,0/5  pounds 

The  stresses  caused  in  the  chord  members  by  this  portion 
of  the  live  load  are  as  follows: 


Member 

Stress,  in  Pounds 

a  b,  dc 

34,870  (tension) 

c  d 

59,780  (tension) 

d  e 

74,720  (tension) 

BC 

59,780  (compression) 

CD 

74,720  (compression) 

DE 

79,700  (compression) 

43.  These  stresses  must  be  increased  to  allow  for  the 
effect  of  impact  and  vibration.  The  increase  is  computed 
by  the  following  formula  (B.  S.,  Art.  99): 

300  -  L 


I  = 


1,000 


X  5 


135—13 


28  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  S77 


As  chord  stresses  are  under  consideration,  the  entire  span 
is  loaded  when  they  are  greatest;  then,  L  =  160,  and,  there¬ 
fore, 


300  -  160 
1,000 


.US 


The  total  live-load  chord  stresses,  in  pounds,  including 
impact  and  vibration,  are  as  follows: 


Member  Tension 

ab,  be  47,600  +  34,870  +  .14  X  34,870  =  87,350 

cd  81,600  +  59,780  +  .14  X  59,780  =  149,750 

de  102,000  +  74,720  +  .14  X  74,720  =  187,180 

Compression 

B  C  81,600  +  59,780  +  .14  X  59,780  =  149,750 

CD  102,000  +  74,720  +  .14  X  74,720  =  187,180 

D  E  108,800  +  79,700  +  .14  X  79,700  -  199,660 

44.  In  computing  the  stresses  caused  in  the  web  mem- 
bers  by  the  load  on  the  car  track,  the  load  at  each  floor- 

beam  is  to  be  taken  as  1,600  p  at  ^5  floorbeams  [ B .  S., 

P 

Art.  98  (4,)].  In  the  present  case,  as  the  panel  length  p  is 
20  feet,  this  gives  1,600  X  20  =  32,000  pounds  at  each  floor- 
beam,  one-half  of  which,  or  16,000  pounds,  is  the  panel  load 
on  one  truss;  and  the  number  of  panel  points  that  must 
be  loaded  is  100  -i-  20  =  5.*  Those  panel  points  must  be 
loaded  that  will  cause  the  desired  stresses  to  be  greatest. 
For  example,  to  find  the  maximum  shear  caused  by  this  por¬ 
tion  of  the  load  in  the  panel  a  b,  the  five  joints  b,  c,  d,  e,  and  d' 
must  be  loaded;  for  the  panel  be,  the  five  joints  c,  d,e,  d',  and 
c',  etc.  must  be  loaded.  When  there  are  less  than  five  panel 
points  to  the  right  of  a  panel,  all  the  joints  to  the  right  are 
loaded,  and  the  remaining  loads  are  considered  to  be  off  the 


*When  - —  does  not  give  a  whole  number,  the  next  larger  whole 

P 

number  must  be  used.  Thus,  if  =  5.34,  this  should  be  called  6. 

P 


§77  DESIGN  OP  A  HIGHWAY  TRUSS  BRIDGE  29 


bridge.  The 
are  as  follows: 

live-load  positive 

shears  due 

to  this  loading 

Panel 

Shear, 
in  Pounds 

Panel 

Shear, 
in  Pounds 

a  b 

50,000 

e  d’ 

12,000 

be 

40,000 

d’  c> 

6,000 

cd 

30,000 

c'b ' 

2,000 

de 

20,000 

b'  af 

0 

45.  These  shears  must  be  increased  to  allow  for  the 
effect  of  impact  and  vibration.  As  before,  the  increase  is 
computed  by  the  formula 

r  _  300  —  L  Q. 

~  1,000“ x 

As  web  stresses  are  under  consideration,  however,  the 
length  of  track  that  is  loaded  to  produce  the  maximum 
stresses  is  different  for  different  members.  It  is  customary 
to  take  for  the  loaded  length  in  this  case  the  distance  from 
the  right-hand  end  of  the  span  up  to  the  first  panel  load, 
or  the  panel  load  that  is  farthest  to  the  left.  Then,  the 
loaded  length  for  the  panel  ab  is  140  feet;  for  the  panel  be , 
120  feet;  for  the  panel  cd,  100  feet;  for  the  panel  de ,  80  feet; 
for  the  panel  ed\  60  feet;  for  the  panel  d'  c' ,  40  feet;  and  for 
the  panel  c'  b' ,  20  feet.  The  total  live-load  positive  shears, 
in  the  different  panels,  including  the  allowances  for  impact 
and  vibration,  are  as  follows: 


Panel 

Shear,  in 

r  Pounds 

a  b 

64,260 

+ 

50,000 

+  .16 

X 

50,000  - 

122,260 

b  c 

48,195 

+ 

40,000 

+  .18 

X 

40,000  = 

95,395 

c  d 

34,425 

+ 

30,000 

+  .20 

X 

30,000  - 

70,425 

de 

22,950 

+ 

20,000 

+  .22 

X 

20,000  = 

47,350 

edf 

13,770 

+ 

12,000 

f  .24 

X 

12,000  - 

28,650 

d'  c’ 

6,885 

+ 

6,000 

+  .26 

X 

6,000  = 

14,445 

c'b ' 

2,295 

+ 

2,000 

+  .30 

X 

2,000  = 

4,895 

b'a' 

0 

46.  Dead-Toad  Stresses. — The  dead  load  consists  of 
the  weight  of  the  floor,  including  the  weight  of  the  stringers 
and  floorbeams,  and  the  weight  of  the  trusses,  including  the 


30  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


lateral  system.  The  weight  of  the  floor,  as  found  in  Art.  19 
and  illustrated  in  Fig.  13,  is  17,694  pounds  at  each  end  of 
each  floorbeam,  that  is,  at  each  panel  point.  As  the  panels 
are  20  feet  On  length,  this  corresponds  to  a  weight  of 
17,694  20  =  884.7,  or  nearly  900  pounds,  per  linear  foot 

for  one  truss.  The  latter  value  will  be  used.  Each  panel 
load  is  then  900  X  20  =  18,000  pounds. 

The  approximate  weight  w  of  one  truss  is  given  by  the 
formula 


w 


(See  B.  A.,  Art.  243) 


jh1  +  2/o5 

12  L  \  100 

in  which  l  —  span; 

W  —  the  total  load  per  linear  foot  supported  by  the 
truss,  exclusive  of  its  own  weight. 

The  dead  load  supported  by  the  truss  was  found  in  the 
preceding  paragraph  to  be  900  pounds  per  linear  foot. 
The  total  live  load  on  the  floor,  due  to  the  uniform  load, 
was  found  in  Art.  41  to  be  1,836  pounds  per  linear  foot, 
or  918  pounds  per  linear  foot  per  truss.  The  load  on  the  car 
track  was  found  in  Art.  42  to  be  1,345  pounds  per  linear 
foot,  or  672.5  pounds  per  linear  foot  per  truss.  Since  the 
stresses  due  to  the  last-named  load  are  increased  to  allow  for 
impact  and  vibration,  it  is  well,  in  calculating  the  load  sup¬ 
ported  by  the  truss,  to  increase  the  live  load  by  the  proper 
amount.  This  gives  the  total  load  coming  to  one  truss  from 
the  car  track,  including  allowance  for  impact  and  vibration, 
as  672.5  +  .14  X  672.5  —  766.65  pounds  per  linear  foot.  Total 
load  W  supported  by  one  truss  is,  then,  900  -f-  918  -f-  766.65 
=  2,584.65  pounds  per  linear  foot;  therefore, 

1  +  2  X  (-160  ~  90 


2,584.65  ,, 

w  =  ■  ■*— — —  X 


12 


\  ioo 


—  426.5  lb.  per  lin.  ft. 


The  panel  load  due  to  the  weight  of  the  truss  is,  then, 
426.5  X  20  =  8,530  pounds,  of  which  one-half,  or  4,265  pounds, 
is  assumed  to  be  applied  at  the  loaded  chord,  and  one-half  at 
the  unloaded  chord  (see  B.  S.,  Art.  97).  The  entire  weight 
of  the  floor  is  taken  at  the  loaded  chord.  The  lateral  system 
will  be  assumed  to  cause  a  panel  load  of  1,000  pounds,  one- 
half  at  each  chord.  Then,  each  panel  load  of  the  unloaded 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  31 

chord  is  4,265  -f  500  =  4,765  pounds,  and  each  panel  load  of 
the  loaded  chord  is  4,765  +  18,000  =  22,765  pounds.  The 
total  dead  panel  load  is  22,765  +  4,765  =  27,530  pounds, 
and  each  reaction  is  96,355  pounds.  The  dead-load  chord 
stresses  are  as  follows: 


Member 

Stress,  in  Pounds 

a  b ,  be 

71,370  (tension) 

c  d 

122,360  (tension) 

de 

152,940  (tension) 

BC 

122,360  (compression) 

CD 

152,940  (compression) 

DE 

163,140  (compression) 

The  dead-load  shears  are  as  follows: 


Panel 

Positive  Shear, 
in  Pounds 

Panel 

Negative  Shear, 
in  Pounds 

a  b 

96,355 

cd 1 

13,765 

b  c 

68,825 

d'e ' 

41,295 

c  d 

41,295 

b' 

68,825 

d  e 

13,765 

V  a' 

96,355 

47.  Wind  Pressure. — In  the  design  of  trusses,  it  is 
customary  to  assume  that  the  maximum  wind  pressure  does 
not  occur  simultaneously  with  the  maximum  live  load,  so 
that  the  stresses  caused  in  the  chord  members  and  end  posts 
of  the  trusses  by  the  wind  pressure  should  not  be  added 
to  the  combined  dead-  and  live-load  stresses  without  some 
additional  allowance.  Practice  varies  as  to  the  method  of 
allowing  for  these  wind  stresses.  It  is  frequently  specified 
that,  when  they  are  less  than  25  per  cent,  of  the  total  com¬ 
bined  dead-  and  live-load  stresses,  the  wind  stresses  may  be 
ignored;  when  greater,  the  members  are  designed  for  the 
sum  of  the  maximum  dead,  live,  and  wind  stresses,  using 
working  stresses  25  per  cent,  greater  than  those  allowed  for 
the  dead-  and  live-load  stresses  alone.  This  method  will  be 
used  here.  As  a  rule,  the  members  are  first  designed  for 
the  combined  dead-  and  live-load  stresses;  the  exposed  area 
of  the  trusses  and  floor,  the  wind  pressure  on  them,  and  the 
stresses  due  to  this  wind  pressure  are  then  calculated,  and 


32  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


the  cross-sections  of  the  members  corrected,  if  necessary,  to 
allow  for  the  wind  stresses. 

48.  longitudinal  Force. — In  this  type  of  bridge,  the 
longitudinal  thrust  of  a  suddenly  stopping  car  is  so  dis¬ 
tributed  throughout  the  length  and  width  of  the  bridge  by 
the  rails,  stringers,  and  floor  plank  that  it  will  not  be  con¬ 
sidered.  If  the  trusses  were  supported  on  a  steel  trestle,  the 
force  would  be  taken  at  the  top  of  the  bent. 

49.  Combined  Stresses. — The  combined  dead-  and 
live-load  stresses  in  the  chord  members  are  as  follows: 

Member  Stress,  in  Pounds 

ab,bc  87,350  +  71,370  —  158,720  (tension) 

cd  149,750  +  122,360  =  272,110  (tension) 

de  187,180  +  152,940  =  340,120  (tension) 

B  C  149,750  +  122,360  =  272,110  (compression) 

CD  187,180  +  152,940  =  340,120  (compression) 

DE  199,660  +  163,140  =  362,800  (compression) 

The  combined  dead-  and  live-load  positive  shears  in  the 
different  panels  are  as  follows: 


Panel 

Shear,  in  Pounds 

a  b 

122,260 

+ 

96,355 

=  218,615 

be 

95,395 

+ 

68,825 

-  164,220 

cd 

70,425 

+ 

41,295 

=  111,720 

de 

47,350 

+ 

13,765 

61,115 

ed' 

28,650 

— 

13,765 

=  14,885 

d'e* 

14,445 

— 

41,295 

=  -  26,850 

As  the  combined  shear  in  the  panel  e  d'  comes  out  positive, 
a  counter  is  required  in  that  panel.  As  the  combined  shear 
in  the  panel  d'  c'  comes  out  negative,  no  counter  is  required 
in  that  panel. 

The  stresses  in  the  diagonals  can  be  found  by  multiplying 
the  shears  in  the  respective  panels  by  esc  H.  The  length  of  a 

diagonal  is  V202  +  27*  =  33.6006,  and  esc  H  =  33.6006  -r  27 
=  1.2445.  Then,  the  stresses  in  the  diagonals  are  as 
follows: 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  33 


Diagonal 
a  B 
Be 
Cd 
De 

Ed'(dE) 


Stress,  in  Pounds 

218,615  X  1.2445  =  272,100  (compression) 
164,220  X  1.2445  -  204,400  (tension) 
111,720  X  1.2445  =  139,000  (tension) 
61,115  X  1.2445  =  76,100  (tension) 
14,885  X  1.2445  =  18,500  (tension) 


The  stresses  in  the  verticals,  except  the  hip  vertical,  are 
each  equal  to  the  sum  of  the  shear  in  the  panel  to  the  right  of 
the  vertical  and  the  dead  load  at  the  top  joint  (4,765  pounds, 
Art.  46).  The  stresses  are  as  follows: 


Member  Stress,  in  Pounds 

Cc  111,720  +  4,765  =  116,500  (compression) 

Dd  61,115  +  4,765  =  65,880  (compression) 

Ee  14,885  +  4,765  =  19,650  (compression) 

According  to  B.  S .,  Art.  98  (2),  the  stress  in  the  hip  ver¬ 

tical  must  be  found  from  the  same  loading  as  the  stress  in 
the  floorbeam.  In  Art.  19,  the  dead  load  on  the  truss  from 
one  floorbeam  was  found  to  be  17,694  pounds;  and  in  Art.  24 


the  live  load,  including  impact  and  vibration,  was  found  to 
be  53,000  pounds.  In  addition,  there  is  a  dead  load  of 
4,765  pounds  at  each  panel  point  of  the  loaded  chord,  making 
the  total  stress  in  the  hip  vertical  17,694  +  53,000  +  4,765 
=  75,459,  or  about  75,500  pounds,  tension. 

The  total  dead-  and  live-load  stresses  in  the  members  are 
shown  in  Fig.  21. 


34  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


DESIGN  OF  MAIN  MEMBERS 

50.  Bottom  Cliord. — The  bottom  chord  will  be  com- 
oosed  of  eyebars  (see  B.  S .,  Art.  139).  The  working  stress 
in  tension  is  given  in  B.  S.,  Art.  103,  as  16,000  pounds  per 
square  inch.  Then,  the  required  net  areas  of  the  bottom 
chord  members  are  as  follows: 


Member 


Required  Net  Area, 
in  Square  Inches 


ab,  be  158,700  4-  16,000  =  9.92 

cd  272,100  -f-  16,000  =  17.01 

de  340,100  +  16,000  =  21.26 

The  required  areas  can  be  made  up  in  a  number  of  ways  by 
using  different  widths  of  eyebars,  and  no  fixed  rule  can  be 
given  for  the  width  that  should  be  u§ed.  In  general,  how¬ 
ever,  eyebars  from  4  to  8  inches  in  width  are  preferable  for 
chord  members  of  highway-bridge  trusses  from  150  to 
175  feet  in  length.  The  smallest  thicknesses  that  can  be 
used  are  given  in  Table  XXX.  The  actual  thickness  should, 
in  general,  be  not  greater  than  about  twice  the  minimum 
thickness,  although  it  is  better  not  to  exceed  the  minimum 
thickness  by  a  very  large  amount.  The  bending  moments 
on  the  pins  are  as  a  rule  less  when  thin  eyebars  are  used 
than  when  thick  bars  are  used. 

1.  Member  de. — In  the  present  case,  four  bars  5  in.  X  ItV  in. 
will  be  used  for  the  member  de.  The  area  of  one  bar  of 
this  size  is  5.3125  square  inches,  and  of  four  bars,  21.25  square 
inches,  which  is  near  enough  to  the  required  area. 

2.  Member  c  d. — For  the  member  c  rf,  four  bars  5  in.  X  i  in. 
will  be  used.  The  area  of  one  bar  of  this  size  is  4.375  square 
inches,  and  of  four  bars,  17.5  square  inches,  which  is  slightly 
greater  than  required. 

3.  Members  ab  and  be. — For  the  members  ab  and  cd ,  it  is 
specified  in  B.  S.,  Art.  139,  that  the  bars  composing  them 
must  be  connected  to  each  other  by  latticing;  this  is  to  make 
these  members  capable  of  resisting  a  small  amount  of  com¬ 
pression,  if  for  any  reason,  sugh  as  a  heavy  wind  storm,  the 
stresses  in  them  are  reversed.  The  method  of  connecting 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  35 

I 

them  by  latticing  is  shown  in  Fig.  22:  an  angle  is  riveted  to 
the  inside  of  each  eyebar,  and  the  outstanding  legs  are  con¬ 
nected  by  single  latticing.  The  area  of  each  bar  so  connected 
must  be  reduced  by  the  area  of  one  rivet  hole;  f-inch  rivets 
will  be  used.  If  two  bars  6  in.  X  1  in.  are  used,  the  gross 
area  of  each  bar  is  6  square  inches,  and  the  net  area  is 
6  —  .875  =  5.125  square  inches;  then,  the  area  of  two  bars  is 


10.25  square  inches.  As  this  is  slightly  greater  than  the 
required  area,  these  bars  will  be  used  for  a  b  and  c  d. 


51.  Inclined  Web  Members. — The  required  net  areas 
of  the  inclined  web  members,  not  including  the  end  post, 
which  will  be  considered  later,  are  as  follows: 


Member 

Required  Net  Area,,  in 

Square  Inches 

Be 

204,400  4-  16,000  -  12.775 

Cd 

139,000  4-  16,000  =  8.69 

De 

76,100  4-  16,000  -  4.76 

dE 

•  18,500  4-  16,000  =  1.16 

Member  Be. — 

-For  Be,  two  bars  6  in.  X  li  in.  will  be 

used.  The  area  of  one  bar  is  6.75  square  inches,  and  of  two 
bars,  13.5  square  inches,  which  is  sufficient. 

2.  Member  Cd. — For  Cd,  two  bars  5  in.  X  i  in.  will  be 
used.  The  area  of  one  bar  is  4.375  square  inches,  and  of 
two  bars,  8.75  square  inches,  which  is  sufficient. 


36  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


3.  Member  D  e. — For  De,  two  bars  3  in.  X  it  in.  will  be 
used.  The  area  of  one  bar  is  2.4375  square  inches,  and  of 
two  bars,  4.875  square  inches,  which  is  sufficient. 

4.  Member  dE. — The  member  dE  is  a  counter,  and, 
according  to  B.  S .,  Art.  141,  cannot  have  a  sectional  area 
less  than  2  square  inches,  although  but  1.16  square  inches  is 
required  by  the  stress.  One  bar  3  in.  X  t  in.  will  be  used; 
its  area  of  cross-section  is  2.25  square  inches,  which  is  greater 
than  2  square  inches. 


52.  Vertical  Web  Members. — The  form  of  cross-sec¬ 
tion  that  is  best  adapted  to  the  compression  web  members 
is  shown  in  Fig.  23.  It  is  composed  of  two  channels  with 
the  flanges  pointing  toward  each  other;  the  flanges  are  con¬ 
nected  by  tie-plates  and  lattice  bars,  as  explained  in  Bridge 
Members  and  Details ,  Part  1.  The  size  of  channel  that  must 


be  used  for  any  member  depends  in  general  on  the  stress 
in  the  member,  but  for  those  verticals  near  the  center  of 
the  span,  in  which  the  stress  is  comparatively  small,  other 
conditions  frequently  govern.  For  example,  it  is  specified 

in  B.  S.,  Art.  105,  that  the  value  of  -  shall  not  exceed  100 

r 

for  main  members.  Since  the  length  of  each  vertical  from 
center  to  center  of  pins  is  27  feet  =  324  inches,  the  smallest 
allowable  value  of  the  radius  of  gyration  r  is  324  -f-  100 
=  3.24  inches.  Consulting  Table  XIII,  it  is  seen  that  the 
smallest  channel  having  a  value  of  r  greater  than  3.24  inches 
is  a  9-inch  13.25-pound  channel.  The  web  of  this  is  only 
.23  inch  thick,  and,  as  it  is  specified  in  B.  S .,  Art.  112, 
that  webs  of  channels  shall  be  not  less  than'!  inch  thick,  this 
channel  cannot  be  used.  A  9-inch  15-pound  channel  is  found 
to  be  the  smallest  channel  that  can  be  used.  Its  radius  of 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  37 


gyration  is  3.4  inches,  and  -  =  —  95.3.  The  gross  area 

r  3.4 

of  two  channels  is  (Table  XIII)  2  X  4.41  =  8.82  square  inches. 
Consulting  Table  XXXV,  the  allowable  working  stress  corre¬ 
sponding  to  a  value  of  -  of  95.3  is  found  to  be  10,640  pounds 

r 

per  square  inch.  Since  the  gross  area  of  two  channels  is 
8.82  square  inches,  the  total  compressive  stress  that  can  be 
resisted  by  a  member  27  feet  long  and  composed  of  two 
9-inch  15-pound  channels  is  8.82  X  10,640  =  93,800  pounds. 
As  this  is  greater  than  the  stress  in  either  D  d  or  Ee ,  these 
channels  will  be  used  for  these  two  members. 

As  the  stress  in  Cc  (+  116,500  pounds)  is  greater  than 
93,800  pounds,  the  two  channels  just  considered  are  not  large 
enough  for  this  member,  and  larger  or  heavier  channels 
must  be  used.  The  radius  of  gyration  of  each  of  the  heavier 
9-inch  channels  is  less  than  the  smallest  allowable  value, 
3.24  inches,  as  found  in  the  preceding  paragraph,  so  that  the 
next  heavier  10-inch  channel,  20  pounds,  will  be  tried.  The 
radius  of  gyration  of  a  10-inch  20-pound  channel  is  given  in 

Table  XIII  as  3.66  inches;  then,  -  =  =  88.5,  and,  by 

r  3.66 

Table  XXXV,  the  allowable  working  stress  is  11,150  pounds 
per  square  inch.  The  gross  area  of  two  channels  is 
(Table  XIII)  2  X  5.88  =  11,76  square  inches,  and. the  total 
stress  that  can  be  resisted  by  two  channels  is  11.76  X  11,150 
=  131,100  pounds.  As  this  is  greater  than  the  stress  in  Cc , 
these  channels  will  be  used  for  this  member. 

53.  Hip  Vertical. — The  stress  in  Bb  is  75,500  pounds,  ten¬ 
sion,  and,  since  the  allowable  working  stress  ( B .  S.,  Art.  103) 
is  16,000  pounds  per  square  inch,  the  required  net  area  of  the 
member  is  75,500  -r-  16,000  =  4.7  square  inches.  The  same 
form  of  cross-section  can  be  used  for  this  member  as  for  the 
other  verticals,  but  that  shown  in  Fig.  24  is  frequently  used, 
and  will  be  employed  here.  The  outstanding  leg  should  be 
at  least  equal  in  width  to  the  outstanding  leg  of  the  floorbeam 
connection  angle.  According  to  B.  S.f  Art.  126,  the 


38  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


connection  angles  cannot  be  less  than  3  inches  wide.  Then, 
3"  X  2a7'  X  tw"  angles  will  be  tried,  as  they  are  the  smallest 
that  can  be  used.  To  get  the  net  area  of  each  angle,  it  will 
be  sufficient  to  deduct  the  area  of  one  hole  for  a  f-inch  rivet 
from  each  angle,  that  is,  .27  square  inch  (Table  XXVII). 
The  gross  area  of  one  angle  is  (Table  X)  1.62  square  inches, 
and  the  net  area,  1.62  —  .27  —  1.35  square  inches.  Then, 
the  area  of  the  member  B  b,  if  composed  of  four  angles,  is 
4  X  1.35  =  5.4  square  inches,  which  is  greater  than  the 
required  value,  and  therefore  sufficient.  It  will  be  found  in 
connection  with  the  details,  however,  that  it  is  advisable  to 


Fig.  24 

use  Si-inch  angles  for  connecting  the  floorbeams  to  the 
verticals.  For  this  reason,  it  is  well  to  use  four  angles 
3^  in.  X  2i  in.  X  ~iw  in.  for  B  b. 


54.  Width,  of  Verticals. — The  width  of  the  hip  vertical 
is  usually  made  about  the  same  as  the  compression  verticals. 
The  channels  that  compose  the  latter  are  placed  far  enough 
apart  so  that  the  radius  of  gyration  about  an  axis  parallel  to 
the  web  is  at  least  equal  to  that  about  an  axis  perpendicular 
to  the  webs.  The  distances  between  the  webs  of  two  chan¬ 
nels  that  form  a  compression  member,  when  the  flanges  are 
turned  outwards,  so  that  the  radii  of  gyration  in  the  two 
directions  will  be  the  same,  is  given  in  column  17,  Table  XIII. 
The  distance  ZX,  Fig.  23,  between  the  backs  of  the  channels 
when  the  flanges  are  turned  inwards  or  toward  each  other 
can  be  found  by  means  of  the  formula 

D'  =■  D  +  4x 

in  which  D  =  distance  found  in  column  17,  Table  XIII; 

jv  =  distance  from  back  of  channel  to  center  of 
gravity,  as  found  in  column  12,  Table  XIII. 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  39 


For  two  10-inch  20-pound  channels,  D'  —  5.97  +  4  X  .61 
=  8.41  inches;  and  for  two  9-inch  15-pound  channels, 
D'  =  5.49  +  4  X  .59  =  7.85  inches.  They  will  be  placed 
8^  inches  apart  in  the  present  case. 

55.  Top  Chord.— ' The  form  of  cross-section  shown  in 
Fig.  25  is  frequently  used  for  the  tpp  chords  and  end  posts 
of  trusses.  The  pins  are  located  near  the  center  of  gravity 
of  the  section,  which  is  nearer  the  top  than  the  bottom;  and, 
in  order  to  provide  room  between  the  pin  and  the  top  cover- 
plate  to  accommodate  the  eyebar  heads,  it  is  sometimes 
necessary  to  use  deeper  chord  members  than  would  otherwise 
be  desirable.  For  this  reason,  this  form  of  cross-section  is 
not  as  desirable  for  light  pin-connected  trusses  as  the  symmet¬ 
rical  form  shown  in  Fig.  26,  in  which  the  center  line  is  located 
a  little  below  the  center  of  gravity.  This  form  will  be  used 


1 

r 

TH 

r  t 

J 

- -  c  - - 

L 

M 

1J 

—  c  - - -*■ 

•  •  . . . . ■'J 

w 

LI 

Fig.  25  Fig.  26 


in  the  present  case.  The  depth  or  width  W  should  be  at  least 
great  enough  to  allow  the  head  of  the  largest  eyebar  to  go 
inside.  The  largest  eyebar  that  connects  to  the  top  chord  is 
6  inches  wide.  In  Table  XXX,  the  sizes  of  heads  for  6-inch 
eyebars  are  given  from  13*  inches  to  15i  inches  in  diameter; 
a  depth  of  15  inches  will  be  tried  first. 

The  distance  c  between  webs  depends  on  the  width  of  the 
vertical  members  and  on  the  arrangement  of  the  ends  of  the 
members  with  respect  to  each  other.  It  is  customary  to 
place  the  heads  of  the  eyebars  that  form  the  main  diagonals 
between  the  vertical  members  and  the  inside  of  the  chord 
members.  As  the  width  of  the  vertical  members  is  8|-  inches 
(Art.  54),  the  clear  distance  c  between  the  webs  of  the  top 
chord  will  be  taken  for  the  present  as  12  inches.  If  neces¬ 
sary,  this  can  be  changed  slightly  when  detailing. 


40  DESIGN  .OP  A  HIGHWAY  TRUSS  BRIDGE  §77 


In  Bridge  Mevibers  and  Details,  Part  1,  it  was  explained 
that,  when,  as  in  this  case,  the  distance  c  is  greater  than 
I  W ,  the  least  radius  of  gyration  is  approximately  equal  to 
3  W,  in  this  case  5  inches.  Since  the  unsupported  length  of 
the  top  chord  members  is  240  inches,  the  approximate  value 

of  -  is  240  -s-  5  =  48,  and  the  allowable  working  stress 
r 

(Table  XXXV)  is  14,180  pounds  per  square  inch.  Then,  the 
trial  values  of  the  required  cross-section  of  the  top  chord 
members  are  as  follows  (see  Fig.  21): 


Member 


Trial  Value, 
in  Square  Inche^ 


BC  272,100  -r-  14,180  =  19.19 

CD  340,100  -h  14,180  =  23.99 

DE  362,800  14,180  -  25.59 

The  top  chord  is  usually  made  in  sections  from  30  to 
60  feet  in  length,  which  are  spliced  in  the  field.  In  the 
present  case,  the  splices  will  be  located  near  D  and  D' , 
Fig.  20,  and  the  chord  will  be  composed  of  three  parts. 

1.  Member  B  C. — For  the  member  B  C,  the  following 


sections  will  be  tried: 

Square 

Inches 

Two  web-plates  15  in.  X  A  in . 9.38 

Four  angles  3i  in.  X  3iin.  X  t  in.  .  .  .  .  .  9.92 

Total . ' . 19.30 


The  flange  angles  will  be  placed  with  the  backs  of  their 
outstanding  legs  15i  inches  apart,  as  shown  in  Fig.  26. 
The  radius  of  gyration  about  axis  X’  X  through  the  center 
of  gravity  of  the  section  is  computed  by  the  method 
explained  in  Bridge  Members  and  Details ,  Part  1,  and  is  found 

to  be  5.67  inches;  the  value  of  -  is  240  5.67  =  42.3;  and 

r 

the  allowable  working  stress  is  14,550  pounds  per  square 
inch.  Then,  the  corrected  value  of  the  required  area  of 
cross-section  is  272,100  —■  14,550  =  18.70  square  inches.  As 
this  is  so  close  to  the  area  tried,  the  assumed  section  will  be 
used  for  B  C. 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  41 


2.  Member  CD. — As  CD  is  a  continuation  of  B  C>  all  the 
simple  sections  of  which  B  C  is  composed  are  also  parts 
of  CD ,  and  any  additional  area  required  for  CD  is  provided 
by  adding  plates.  The  flange  angles  are  far  enough  apart 
to  allow  an  8-inch  vertical  plate  between  the  vertical  legs  of 
the  angles,  as  shown  at  a, a  in  Fig.  27.  The  following 
section  will  be  tried  for  CD: 

Square 


Inches 

Two  web-plates  15  in.  X  in .  9.3  8 

Four  angles  3i  in.  X  3i  in.  X  fin .  9.9  2 

Two  vertical  plates  8  in.  X  it  in .  5.0  0 

Total  . 2  4.3  0 


The  radius  of  gyration  with  reference  to  the  axis  X'X 
through  the  center  of  gravity 
of  the  section  is  found  to  be 

5.16  inches;  the  value  of  -  is 

r 

240  -h  5.16  =  46.5;  and  the  al¬ 
lowable  working  stress  is  14,290 
pounds  per  square  inch.  Then, 
the  corrected  value  of  the 
required  area  of  cross-section  is  340,100  -j-  14,290  =  23.80 
square  inches.  As  this  is  so  close  to  the  area  tried,  the 
assumed  section  will  be  used  for  CD. 

3.  Member  D  E. — For  member  D  E,  the  same  form  will 
be  used  as  for  CD.  The  following  section  will  be  tried: 


Square 

Inches 

Two  web-plates  15  in.  X  in .  9.3  8 

Four  angles  3i  in.  X  3i  in.  X  I  in.  .  9.9  2 

Two  vertical  plates  8  in.  X  in .  7.0  0 

Total  . 2  6.3  0 


The  radius  of  gyration  with  reference  to  X'  Xis  5.01  inches; 

the  value  of  -  is  240  -r-  5.01  =  47.9;  and  the  allowable  work- 
r 

ing  stress  is  14,170  pounds  per  square  inch.  Then,  the 
corrected  value  of  the  required  area  of  cross-section  is 


m 


J  Center  of 
Gravity 

J 


a 


Fig.  27 


42  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 

-362,800  4-  14,170  =  25.60  square  inches.  As  this  is  so  close 
to  the  area  tried,  the  assumed  section  will  be  used  for  DE. 

5G.  End  Post. — The  end  post  will  be  made  of  the  same 
general  form  as  the  top  chords.  The  unsupported  length 
of  the  end  post  is  33.6  feet,  or  403.2  inches;  the  radius  of 
gyration  will  be  assumed  equal  to  5  inches.  The  value  of 

the  ratio  -  is,  then,  403.2  4-  5  —  80.6,  and  the  allowable 
r 

working  stress  is  11,760  pounds  per  square  inch.  There¬ 
fore,  the  trial  value  of  the  required  area  of  cross-section  is 
272,100  4-  11,760  —  23.14  square  inches.  The  same  section 
will  be  used  for  this  member  as  for  the  top  chord  mem¬ 
ber  CD,  unless  it  is  necessary  to  revise  the  section  later 
on  account  of  the  wind  stresses. 


DESIGN  OF  LATERAL  SYSTEM 


WIND  STRESSES 

57.  Introductory  Statement.-— Before  designing  the 
details,  it  is  advisable  to  compute  the  wind  stresses,  so  that, 
if  necessary,  the  sections  of  the  main  members  may  be 
changed.  The  lateral  system  will  also  be  designed  at  this 
time. 

58.  Wind  Pressure. — The  wind  pressure  will  be  taken 
as  50  pounds  per  square  foot  on  twice  the  exposed  area 
of  one  truss  together  with  the  floor  {B.  S.,  Art.  100).  In 
calculating  the  exposed  area  of  a  member,  it  is  customary 
to  multiply  its  width  by  the  distance  between  the  centers  of 
its  connections.  In  tension  members  composed  of  eyebars, 
the  width  of  the  eyebar  is  used;  in  built-up  members,  1  inch 
is  added  to  the  depth  of  the  web  or  channel,  or  the  width  of 
angles,  to  allow  for  the  latticing.  The  exposed  widths  of 
the  members  at  one  end  of  the  truss  are  as  follows  (see 
Fig.  20):  for  a  B ,  B  C,  CD,  and  D  E,  16  inches;  for  B  b, 
7  inches;  for  Cc ,  11  inches;  for  D  d  and  Ee ,  10  inches;  for 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  43 


Ac,  6  inches;  for  Cd,  5  inches;  for  D e  and  Ed,  3  inches;  for 
a  b  and  be,  6  inches;  and  for  cd  and  de,  5  inches.  Multiply¬ 
ing  each  of  these  widths  by  the  length  of  the  member,  the 
exposed  area  of  the  upper  chord  of  one  truss  is  found  to  be 
160  square  feet;  of  the  lower  chord,  73.33  square  feet;  and 
of  the  web  members,  333.3  square  feet.  Then,  the  wind 
pressure  on  twice  the  exposed  area  of  one  truss  on  the  top 
chords  is 

2  X  160  X  50  =  16,000  pounds; 
on  the  bottom  chords, 

2  X  73.3  X  50  =  7,330  pounds; 
and  on  the  web  members, 

2  X  333.3  X  50  =  33,330  pounds 
The  exposed  area  of  the  floor  is  equal  to  the  length  of  the 
span  (160  feet)  multiplied  by  the  vertical  distance  from  the 


highest  portion  of  the  floor  (the  edge  of  the  sidewalk)  to 
the  bottom  of  the  lowest  I  beam,  about  3  feet,  Fig.  5.  It  is, 
therefore,  160  X  3  =  480  square  feet,  and  the  wind  pressure 
on  it  is  480  X  50  =  24,000  pounds.  The  wind  pressure  on 
the  railings  will  be  taken  as  75  pounds  per  linear  foot,  or 
75  X  160  =  12,000  pounds  on  the  entire  length  of  railings. 

59.  Upper  Lateral  Truss. — The  upper  lateral  truss  is 
shown  in  Fig.  28.  It  is  customary  to  assume  that  the  wind 
pressure  on  the  top  chord  and  one-half  that  on  the  web 
members — in  this  case,  16,000  +  33,330  ~  2  =  32,665  pounds 
— is  resisted  by  the  top  lateral  truss.  Since  the  top  chord  is 

135—14 


t 


44  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 

120  feet  Ion",  this  corresponds  to  32,665  -r-  120  —  272.2  pounds 
per  linear  foot,  and  the  load  per  panel  is  272.2  X  20 
=  5,444pounds,  as  represented  in  Fig-.  28.  For  convenience, 
the  entire  panel  load  is  assumed  to  be  applied  at  the  wind¬ 
ward  side.  There  are  also  to  be  considered  the  two  hall- 


panel  loads  of  2,722  pounds  each  at  B  and  B'.  The  wind 
stresses  in  the  upper  lateral  truss  are  shown  in  Fig.  29. 

60.  Dower  Lateral  Truss.— The  lower  lateral  truss  is 
clearly  shown  in  Fig.  30.  It  is  customary  to  assume  that 
the  wind  pressure  on  the  railings,  the  floor,  the  bottom 
chord,  and  one-half  that  on  the  web,  which  in  this  case  is 


12,000  +  24,000  +  7,330  +  33,330  -s-  2  -  60,000  pounds,  is 
resisted  by  the  bottom  lateral  truss.  As  the  bottom  chord 
is  160  feet  long,  this  corresponds  to  60,000  ■—  160  =  375 
pounds  per  linear  foot.  The  panel  load  is  375  X  20  —  7,500 
pounds,  as  shown  in  Fig.  30.  For  convenience,  all  the  panel 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  45 


load  is  assumed  to  be  applied  at  the  windward  side.  The 
half-panel  loads  at  a  and  a'  will  be  neglected;  they  are 


transmitted  directly  to  the  abutments  by  the  pedestals.  The 
stresses  in  the  lower  lateral  truss  are  shown  in  Fig.  31. 

61.  Portal  and  Transverse  Frames. — The  depth  of 
the  portal  and  transverse  frames  depends  on  the  amount  of 
room  above  the  overhead  clearance  line,  and  this  in  turn 
depends  on  the  position  of  the  floor.  In  the  present  case, 
as  the  allowable  distance  from  the  top  of  the  floor  to  the 
underneath  clearance  line  is  6  feet  (Art.  1),  the  floorbeams 
will  be  connected  to  the  vertical  posts  above  the  pins,  leaving 
the  lower  chord  to  project  a  short  distance  below  the  floor- 
beams.  To  clear  the  main  diagonals,  which  will  be  outside 
the  vertical  posts,  as-  will  be  shown  in  Design  of  a  High¬ 
way  Truss  Bridge ,  Part  2,  the  bottom  of  the  floorbeam 
will  be  placed  1  foot  above  the  center  of  the  pins  in  the 
lower  chord.  It  will  be  seen  later,  in  connection  with 
the  details,  that  the  top  of  the  floor  at  the  center  of  the 
bridge  is  9  inches  above  the  top  of  the  floorbeam;  as  the 
floorbeam  is  3  feet  64  inches  deep,  the  top  of  the  floor  is 
9  inches  3  feet  64  inches  +  1  foot  =  5  feet  34  inches  above 
the  center  of  the  lower  chord,  and  27  feet  —  5  feet  34  inches. 
=  21  feet  8f  inches  below  the  center  of  the  top  chord.  As 
this  is  more  than  20  feet,  transverse  frames  are  required  at 
each  panel  point  ( B .  S.,  Art.  159). 

In  B.  S.,  Art.  94,  the  required  headroom  is  specified  as 
15  feet.  This  leaves  6  feet  8f  inches  from  the  overhead 


46  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


clearance  line  to  the  center  of  the  top  chord.  The  top  laterals 
are  connected  to  the  top  of  the  top  chord  about  8  inches  from 

* - 28  L0" - * 


Top  of  Top  CLore/ 


I 

r 

* 

N 

* 

1 

S* 

> 

5 

oy 

Of  d 

1 

% 

1 

i 

> 

4 

5 

r% 

\ 

- a, 

- 5 

5 

* 

■> 

' 

T 

of  Lower  C/?ora' 

Pig.  32 


the  center  of  the  chord,  making  the  total  depth  of  the  trans¬ 
verse  frames  about  6  feet  8f  inches  +  8  inches  —  7  feet 
4i  inches.  Curved  brackets  will  be  placed  at  each  end  of 


each  transverse  frame.  Since  the  edges  of  the  wheel-guards 
are  1  foot  8  inches  from  the  center  of  the  trusses,  the  brackets 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  47 


will  extend  4  feet  6  inches  from  the  center  of  the  trusses 
(B.  S .,  Art.  94).  They  will  also  be  made  about  4  feet 
6  inches  in  depth,  as  represented  in  Fig.  32,  which  is  a  cross- 
section  of  the  bridge  showing  a  type  of  frame  and  bracket 
adapted  to  the  present  case.  The  holes  a ,  a  in  the  curved 
brackets  are  simply  for  ornamentation. 

The  same  general  type  of  frame  will  be  used  for  the 
portal,  as  represented  in  Fig.  33.  The  brackets  will  extend 
4  feet  6  inches  out  from  the  center  of  the  trusses;  the  other 
dimensions  shown  in  Fig.  33  are  found  from  those  shown  in 
Fig.  32  by  multiplying  the  latter  by  esc  H  (1.2445). 


62.  The  force  that  acts  on  the  portal  is  one-half  the  total 
wind  pressure  on  the  upper  chord,  or  16,330  pounds.  Making 
use  of  the  formulas  given  in  Stresses  in  Bridge  Trusses ,  Part  5, 
assuming  the  point  of  inflection  of  the  end  post  to  be  half 
way  between  the  bottom  of  the  bracket  and  the  bottom  of  the 
post,  the  required  stresses  are  found  to  be  as  follows: 

Direct  stress  in  end  posts, 

Phi  16,330  X  24.63 


b  28 

Bending  moment  on  end  posts, 
P 


14,360  pounds 


{/ d  —  d  —  d')  —  8,165  X  9.8  X  12  =  960,200  inch-pounds 


Direct  stress  in  each  web  diagonal, 
P/d  l  =  16,330  X  24.63  X  11.12 
nbd  6x28x9.20 

The  stress  in  the  top  flange  is 


=  2,894  pounds 


P/d  P 
2d  +  2 


P  Id  x 
~  bd 


At  the  section  opposite  D,  x  =  4.5,  and  the  stress  is 
16,330  X  24.63  16,330  _  16,330  X  24.63  X  4.5 

2  X  9.20  +  2  28  X  9.20 

=  23,000  pounds,  compression 
At  the  section  opposite  D\  x  —  23.5,  and  the  stress  is 
16,330  X  24.63  16,330  _  16,330  X  24.63  X  23.5 

2  X  9.20  +  ”  2  28  X  9.20 

=  —  6,640  pounds,  tension 


48  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 


The  stress  in  the  bottom  flange  at  D  is 

16,330  X  24.63  _  16,330  X  24.63  X  4,5 
2  X  9.20  28  X  9.20 

=  14,800  pounds,  tension 
The  stress  in  the  bottom  flange  at  D'  is 

16,330  X  24.63  _  16,330  X  24.63  X  23.5 
2  x  9.20  28  X  9.20 

=  14,800  pounds,  compression 
There  is  also  a  direct  stress  caused  in  the  bottom  chord  of 
the  main  truss  by  the  direct  stress  in  the  end  post;  the 
former  is  found  by  multiplying  the  latter  by  cos  H  (20  -*•  33.6 
=  .5952);  this  gives  14,360  X  .5952  =  8,550  pounds.  This 
stress  is  tension  on  the  leeward  side,  which  is  the  only  side 
that  will  be  considered,  since  the  compression  on  the  wind¬ 
ward  side  simply  decreases  the  tension  in  the  chord. 


DESIGN  OF  MEMBERS  . 

63.  Upper  Lateral  Truss. — Comparing  the  wind 
stresses  in  the  top  chord  members  with  the  combined  dead- 
and  live-load  stresses,  it  is  seen  that  the  former  are  less  than 
25  per  cent,  of  the  latter,  and  need  not  be  further  considered 
(Art.  47). 

The  diagonals  are  usually  composed  of  one  angle;  in  the 
present  case,  the  required  net  area  in  the  end  panel  is 
16,730  --  16,000  =  1.05  square  inches.  The  net  area  of  a 
2k"  X  2V'  X  iV7  angle,  after  deducting  one  f-inch  rivet  hole, 
is  1.2  square  inches,  which  is  sufficient.  If  this  angle  is 
used,  however,  the  bending  stress  due  to  its  own  weight  is 
greater  than  the  allowable  intensity  of  bending  stress;  so 
that  a  larger  angle  must  be  used.  For  this  reason  one 
3!"  X  X  Te"  angle  will  be  used  for  each  diagonal  in  each 
panel,  the  longer  leg  being  placed  vertical. 

64.  The  rivets  connecting  the  laterals  to  the  connection 

plates  are  f-inch  rivets,  field  driven,  and  in  single  shear,  the 
value  being  3,980  pounds.  Then,  the  number  of  rivets 
required  at  each  end,  since  the  greatest  stress  is  16,730 
pounds,  is  16,730  3,980  =  4.2,  or,  say,  5  rivets.  In  the  next 


§  77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


40 


two  panels,  three  rivets  and  one  rivet  are  sufficient,  respect¬ 
ively,  but  five  rivets  will  be  used,  the  same  as  in  the  end  panel. 

65.  The  maximum  stress  in  a  transverse  strut  is  shown 
in  Fig.  29  to  be  13,610  pounds.  It  is  customary  to  design 
the  upper  flange  of  the  frames  shown  in  Fig.  32  to  resist  this 
stress,  and  to  make  the  lower  flange  the  same  size  as  the 
upper.  In  B.  S.,  Art.  105,  it  is  specified  that  no  lateral 

member  shall  have  a  ratio  of  -  greater  than  120.  In  the 

r 

present  case,  since  /  is  28  feet,  it  is  advisable  to  insert  one 
2i"  X  X  iV'  angle  connecting  the  center  of  each  trans¬ 
verse  strut  with  the  intersections  of  the  diagonals,  as  shown 
by  the  dotted  lines  a  a  in  Fig.  29,  thereby  reducing  the 
value  of  l  to  14  feet,  or  168  inches.  Then,  the  smallest 
allowable  value  of  r  is  168  -4-  120  =  1.4  inches.  The  top 
flange  of  the  frame  will  be  made  of  two  angles,  with  their 
backs  spaced  -fe  inch  apart.  Consulting  Table  XXVI,  it  is 
seen  that  the  smallest  angles  that  can  be  used  are  two  angles 
3  in.  X  in.  X  A  in.,  for  which  the  radius  of  gyration  is 
1.44  inches  when  the  short  legs  are  placed  t5w  inch  apart. 
These  angles  are  found  to  contain  sufficient  area. 

66.  Lower  Lateral  Truss. — In  the  design  of  the  upper 
lateral  truss,  it  was  found  that  the  smallest  angle  that  can 
be  used  for  a  diagonal  is  3i  in.  X  2i  in.  X  t&  in.  The  net 
area  of  such  an  angle,  after  deducting  one  t-inch  rivet  hole, 
is  1.51  square  inches,  and  its  value  in  tension  is  1.51  X  16*000 
—  24,160  pounds.  This  angle  can  be  used  in  all  but  the 
end  panel. 

The  number  of  rivets  required  to  connect  the  angle  in  the 
panel  be  at  each  end,  since  the  stress  is  23,040  pounds  and 
the  value  of  one  rivet  (f-inch  rivet,  field  driven,  and  in  single 
shear)  is  3,980  pounds,  is  23,040  -f-  3,980  =  5.8,  or,  say, 
6  rivets.  Six  rivets  will  be  used  in  the  panel  be ,  and  also, 
to  make  the  laterals  alike,  in  the  panels  cd  and  de. 

The  tension  in  the  diagonal  in  the  panel  ab  is  32,260 
pounds,  and  the  required  net  area  is  32,260  16,000  =  2.02 

square  inches.  One  angle  4  in.  X  3  in.  X  I  in.  will  be  used; 


50  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §77 

the  net  area,  after  deducting  one  i-inch  rivet  hole,  is  2.15 
square  inches.  The  number  of  rivets  required  to  connect 
the  lateral  at  each  end,  since  the  value  of  one  rivet  is  3,980 
pounds,  is  32,260  -f-  3,980  =  8.1,  or,  say,  9  rivets. 

Lug  angles  will  be  placed  on  all  the  lateral^.  The  end  of 
the  lateral  that  has  just  been  designed  is  shown  in  Fig.  34. 

67.  It  is  unnecessary  in  this  case  to  consider  the  wind 
stresses  in  the  floorbeams,  such  as  +  26,250  pounds  in  bb'\ 
they  usually  increase  the  intensity  of  stress  in  the  floorbeam 
by  a  very  small  amount,  which  can  be  neglected. 

68.  In  comparing  the  wind  stresses  in  the  lower  chord 
members  with  those  due  to  dead  and  live  loads,  it  is  necessary 
to  add  the  stress  in  the  leeward  chord  that  is  caused  by  the 
direct  stress  in  the  end  post  (8,550  pounds,  tension)  to  the 


stresses  in  the  leeward 
chord  members  due  to 
their  positions  as  mem¬ 
bers  of  the  lower  lateral 
stress.  In  the  present 
case,  none  of  the  wind 
stresses  in  the  lower 


/  /L  ^"x3"x§r 


Fig.  34 


chord  members  is  so  great  as  25  per  cent,  of  those  due  to 
combined  dead  and  live  loads,  and  so  they  will  not  be 
further  considered. 

69.  Portal. — The  direct  stress  in  a  lattice  bar  was 
found  in  Art.  62  to  be  2,894  pounds.  As  the  stress  in  any 
one  of  these  bars  is  compression  when  the  wind  comes  from 
one  direction,  and  tension  when  it  comes  from  the  other, 
each  must  be  designed  for  2,894  -J-  .8  X  2,894  =  5,209  pounds, 
tension  and  compression  ( B .  Art.  107).  Flat  bars  are 
sometimes  used  for  the  diagonals,  but  when  the  depth  of 
portal  is  greater  than  about  3  feet  it  is  better  to  use  small 
angles,  as  they  give  greater  stiffness  to  the  web.  In  the 
present  case,  one  2"  X  2"  X  angle  will  be  used  for  each 
diagonal.  This  is  smaller  than  the  smallest  allowable  angle, 
as  given  in  B.  S.,  Art.  113,  but,  since  this  may  be  considered 


77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  51 


an  unimportant  detail,  it  will  be  used.  Each  end  will  be 
connected  by  two  f-inch  rivets.  The  same-sized  angles  will 
be  used  for  the  lattice  web  of  the  transverse  struts. 

The  stress  in  the  top  flange  was  found  in  Art.  G2  to  be 
23,000  pounds  compression  at  one  end,  and  6,640  pounds 
tension  at  the  other  end.  When  the  wind  blows  in  the 
opposite  direction,  these  stresses  are  reversed.  The  top 
flange  should  therefore  be  designed  for  23,000  -f  .8  X  6,640 

=  28,310  pounds  compression,  and  6,640  +  .8  X  23,000 

* 

=  25,040  pounds  tension.  The  center  of  the  top  flange 
will  be  held  by  one  2^"  X  2i"  X  iV'  angle  in  the  same  way 
as  the  transverse  frames,  as  shown  at  b,  Fig.  29,  thereby 
reducing  the  unsupported  length  to  14  feet,  or  168  inches. 
The  smallest  allowable  value  of  r  is,  then,  168  —  120  =  1.4 
inches.  The  smallest  angles  that  can  be  used  are  two 
3"  X  2|"  X  !%"  angles,  for  which  the  radius  of  gyration  is 
1.44  inches.  These  angles  are  found  to  have  sufficient  area, 
and  so  will  be  adopted. 

The  stress  for  which  the  bottom  flange  should  be  designed 
is  14,800  +  .8  X  14,800  =  26,600  pounds  tension  and  com¬ 
pression.  The  same-sized  angles  will  be  used  here  as  for 
the  top  flange,  that  is,  two  3"  X  2i"  X  tV"  angles,  with  the 
2o-inch  legs  t*?  inch  apart  and  the  3-inch  legs  outstanding. 

There  is  no  need  to  design  the  bracket.  It  is  customary  to 
use  a  web  about  inch  thick  and  angles  on  three  sides 
about  the  same  size  as  those  in  the  flanges  of  the  portal. 

70.  Effect  of  Wind  Stresses  on  End  Post. — On 
account  of  the  bending  moment  on  the  end  post,  it  is  not 
sufficient  to  see  that  the  direct  stress  due  to  the  wind  does 
not  exceed  25  per  cent,  of  the  combined  dead-  and  live-load 
stresses,  but  it  must  be  seen  in  every  case  that  the  maximum 
intensity  of  stress  due  to  the  combined  direct  and  bending 
stresses  does  not  exceed  the  allowable  working  stress  by 
more  than  25  per  cent.  The  formula  used  in  the  determination 
of  the  maximum  intensity  of  stress  s  is 

S  Me 

A+  /  ^ 


s 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


K»> 

t)j 


<  < 


in  which  S'  =  combined  dead,  live,  and  wind  direct  stresses; 

A  =  gross  area  of  member; 

M  =  bending  moment  due  to  wind; 
c  =  distance  of  extreme  fiber  from  center  of  end 
post,  measured  at  right  angles  to  truss; 

/  =  moment  of  inertia  of  cross-section  of  end 
post  about  an  axis  parallel  to  webs  and 
half  way  between  them. 

In  the  present  case,  A  =  272,100  (Art.  49)  +  14,360 
(Art.  62)  =  286,500  pounds,  and  M  =  960,200  inch- 
pounds  (Art.  62).  For  the  section  that  was  decided  on 
in  Art.  56,  A  —  24.3  square  inches,  c  —  6  -f-  -ft-  +  3i 
=  9if  inches,  and  /  =  1,108.  Then,  the  actual  intensity 
of  stress  s  is 


286,500  .  960,200  X  9.81  on  ,nn  ,  .  , 

- — - 1 - - - - -  =  20,300  pounds  per  square  inch 

24.3  1,108 

The  allowable  working  stress  in  the  end  post,  without 
considering  the  effect  of  the  wind,  is  given  in  Art.  56  as 
11,760  pounds  per  square  inch.  When  the  wind  is  consid¬ 
ered,  the  allowable  working  stress  is  25  per  cent,  greater 
than  this,  or  11,760  -f-  .25  X  11,760  =  14,700  pounds  per 
square  inch.  As  this  is  much  less  than  the  actual  intensity 
of  stress,  20,300  pounds  per  square  inch,  it  is  necessary  to 
increase  the  section  of  the  end  post.  The  following  section 
will  be  tried: 


Square 


Inches 

Two  web-plates  15  in.  X  ft-  in.  . . 1  3.1  2 

Four  angles  3i  in.  X  3a  in.  X  i  in . 1  3.0  0 

Two  side  plates  8  in.  X  i  in .  8.0  0 

Total . 3  4.12 


The  least  radius  of  gyration  of  this  section  is  5.03  inches,  and 
since  the  unsupported  length  of  the  end  post  is  403.2  inches, 

the  value  of  -  is  80.2.  By  Table’  XXXV,  the  allowable  work- 

r 

ing  stress  for  combined  dead-  and  live-load  stresses  is 
11,790  pounds  per  square  inch.  Increasing  this  25  per 
cent,  gives  14,740  pounds  per  square  inch  as  the  allowable 


§77  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  53 


working  stress  for  combined  dead,  live,  and  wind  stresses. 
The  clear  distance  between  webs  will  be  made  Ilf  inches,  or 
i  inch  less  than  the  top  chord;  this  will  bring  the  vertical 
legs  of  the  flange  angles  Ilf  +  =  12f  inches  apart, 

the  same  as  in  the  top  chord,  and  the  extreme  fiber  6.31  +  3.5 
=  9.81  inches,  from  the  center  of  the  section.  '  Then,  the 
moment  of  inertia  about  an  axis  parallel  to  the  web  is 
1,553.  Substituting  the  new  values  in  the  formula  gives 

286,500,960,200  x  9.81  1A  ,-n  ,  .  , 

s  =  -  —  +  - — ! — — tA - =  14,470  pounds  per  square  inch 

34.12  1,553 

As  this  is  less  than  the  allowable  working  stress,  14,740 
pounds  per  square  inch,  the  section  that  has  been  tried  is 


sufficient,  and  will  be  adopted.  It  is  not  necessary  to  com¬ 
pute  the  shearing  stress  caused  in  the  end  post  by  the  wind 

/ 

when  the  bending  moment  is  considered. 

71.  The  sections  that  have  been  decided  on  for  the  vari¬ 
ous  members  of  the  vertical  trusses  are,  for  convenience, 
shown  on  the  members  in  Fig.  35. 


DESIGN  OF  A  HIGHWAY 
TRUSS  BRIDGE 

(PART  2*) 


DETAILS 


FLOOR  CONNECTIONS 

1.  Cross-Section. — The  location  of  the  top  of  the 
floor  with  respect  to  the  top  of  the  floorbeam  is  shown  in 
Fig-.  1.  It  is  customary  to  keep  the  top  flange  of  the  floor 
beam  as  high  as  it  is  possible  to  have  it  without  interfering 
with  the  floor  plank.  This  can  be  done  by  so  placing  the 
stringers  d ,  e ,  and  /  under  the  roadway  that  their  top  flanges 
are  very  near  the  top  of  the  floorbeam,  and  making  the  nail¬ 
ing  pieces  i  on  top  of  the  stringers  d  at  the  edge  of  the  road¬ 
way  of  sufficient  thickness  to  bring  the  bottom  of  the  floor 
plank  at  the  lowest  pointy  above  the  top  of  the  floorbeam. 

In  Fig.  1,  the  three  roadway  stringers  d ,  e ,  and  /  are  placed 
with  their  tops  1  inch  below  the  top  of  the  floorbeam'  and 
the  top  of  the  wheel-guard  is  placed  1  foot  above  the  top  of 
the  floorbeam.  This  makes  the  nailing  piece  on  stringer  d 
about  2  inches  thick,  and  brings  the  bottom  of  the  3-inch 
plank  at  j  about  1  inch  above  the  top  of  the  floorbeam.  As 
the  sidewalk  plank  rises  -4  inch  per  foot  toward  the  railing, 
the  distance  from  the  top  of  the  sidewalk  bracket  (level  with 

x'The  abbreviation  B .  .S’,  stands  for  Bridge  Specifications ,  to  which 
.Section  frequent  reference  is  made  in  this  and  in  some  of  the  following 
Sections.  All  tables  referred  to  are  found  in  Bridge  Tables ,  unless 
otherwise  stated. 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIOHTS  RESERVED 

§78 


2 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


8&pug 


the  top  of  the  floor- 
beam)  to  the  top  of 
the  sidewalk  plank  at 
stringer  c  is  about  12f 
inches;  this  makes  it 
possible  to  place  the 
sidewalk  stringers  b 
and  c,  9  inches  deep,  on 
top  of  the  top  flange 
of  the  bracket,  leaving 
room  for  a  nailing  piece 
about  If  inches  in  thick¬ 
ness  on  top  of  stringers. 

2.  The  location  of 

the  tops  of  the  stringers 

g  and  h  under  the  car 

track  depends  on  the 

6  crown  of  the  roadway 

and  on  the  depth  of  rail 

and  tie.  It  has  been 

stated  ( Design  of  a 

Highway  Truss  Bridge , 

Part  1)  that  the  wheel¬ 
er 

^  guard  would  be  placed 
6  inches  above  the  floor 
^  at  the  edge  of  the  road- 
<§  way,  and  the  floor  given 
a  crown  of  3  inches, 
bringing  the  top  of  the 
floor  at  the  center  of  the 
bridge  (level  with  the 
top  of  the  rail)  3  inches 
below  the  wheel-guard; 
since  the  latter  is  12 
inches  above  the  top  of 
the  floorbeam,  the  top 
•  of  the  rail  is  9  inches 


§  78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


above  the  top  of  the  floorbeam,  as  shown  in  Fig.  1.  If  the 
rails  are  7  inches  high,  and  the  ties  are  framed  to  5i  inches 
in  depth  where  they  bear  on  the  stringers,  the  tops  of  the 
stringers  will  be  7  -f-  52  =  12i  inches  below  the  top  of  the 
floor,  and  12i  —  9  =  3-2  inches  below  the  top  of  the  floorbeam. 

3.  Connection  of  Fence  and  Fascia  Girders  to  End 
of  Bracket. — The  detail  of  the  connection  of  the  fence  and 
fascia  girders  to  the  end  of  the  sidewalk  bracket  is  shown  in 
Fig.  2:  (a)  is  the  elevation  of  the  fence  and  fascia  girder, 
and  (b)  is  the  cross-section  of  fence  and  fascia  girder  and 
elevation  of  end  of  bracket.  This  is  a  very  popular  and  ser¬ 
viceable  type  of  fence;  it  consists  of  a  number  of  flat  bars  a,  a 
crossing  each  other  at  intervals  to  form  a  lattice  web  and  held 
at  their  intersections  by  small  ornamental  castings  b.  Near 
the  top  and  bottom  of  the  fence  are  pairs  of  longitudinal 
angles  c ,  c>  about  2  in.  X  2  in.  X  i  in.  The  fence  posts  d,  d 
are  usually  composed  of  two  angles  2i  in.  X  2i  in.  X  Ar  in., 
and  enclose  the  web  e  at  the  end  of  the  bracket;  the  fence  and 
fascia  girders  are  riveted  to  the  outstanding  legs  of  the  fence 
angles,  as  shown  at  (a).  The  rivets  are  f  inch  in  diameter 
and  spaced  about  2J  inches  apart  at  /,  the  connection  of  the 
fence-post  angles  to  the  web  of  the  bracket;  above  the  bracket, 
the  angles  are  connected  to  each  other  by  means  of  a  rivet 
every  10  or  12  inches,  a  washer^  of  the  same  thickness  as 
the  web  e  being  inserted  between  the  angles  at  each  rivet. 
The  rivets  h  in  the  connection  of  the  fascia  girder  to  the  fence 
post  are  spaced  about  4i  inches  apart;  those  in  the  top  and 
bottom  flanges  of  the  fascia  girder  are  spaced  about  6  inches 
apart.  In  locating  the  rivet  holes  for  the  connection  of  the 
fence  posts  to  the  bracket,  the  clear  width  of  sidewalk  can 
be  made  just  6  feet,  as  required. 

4.  Connection  of  Sidewalk  Stringers  to  Brackets. 
The  sidewalk  stringers  b  and  c,  Fig.  1,  are  made  about  1  inch 
shorter  than  the  panel  length,  so  as  to  leave  some  clearar.ce 
between  the  ends  of  the  stringers  over  the  bracket.  The 
ends  of  the  stringers  are  connected  to  each  other,  as  shown 
in  Fig.  3,  by  means  of  two  plates  d,  Ar  inch  thick,  riveted  to 


(N 

e 

£ 


4 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  5 

the  webs  of  both  beams.  In  the  figure'  (a)  is  the  cross- 
section  of  the  top  flange  of  the  bracket  and  the  elevation 
of  the  adjacent  ends  of  the 
stringers;  (b)  is  a  longitudi¬ 
nal  section  on  the  line  cc, 
and  shows  the  plan  of  the 
bottom  flanges  of  the  string¬ 
ers  and  the  top  flange  of  the 
bracket.  The  lower  flanges 
of  the  stringers  are  riveted 
to  the  upper  flanges  of  the 
brackets,  as  shown  at  e. 

Under  each  sidewalk  string¬ 
er,  a  pair  of  stiffener  angles  /, 

2i  in.  X  2i  in.  X  in.,  and 
about  15  inches  long,  are 
riveted  to  the  web  of  the 
bracket.  The  reaction  from 
the  stringers  is  so  small  that 
it  is  not  necessary  to  calcu¬ 
late  the  number  of  rivets 
required  in  the  stiffener;  it  is  customary  to  place  five  or 
six  rivets  in  each. 

5.  Connection  of  Roadway  Stringers  to  Floorbeam. 
The  roadway  stringers  d,e,  and  /,  Fig.  1,  are  riveted  to  the 
web  of  the  floorbeam  by  means  of  connection  angles  d, 
Fig.  4;  and  short  shelf  angles  e,  e,  and  stiffeners  /,  /  are 
placed  under  them.  In  Fig.  4,  (a)  is  the  cross-section  of  a 
part  of  the  top  of  the  floorbeam  and  an  elevation  of  the  ends 
of  two  stringers  resting  on  the  shelf  angles;  (b)  is  a  longi¬ 
tudinal  section  on  cc  and  a  plan  of  the  bottom  flanges  of  the 
stringers.  The  upper  parts  of  the-  stringers  z ,  i  are  cut  back 
to  clear  the  vertical  legs  of  the  floorbeam  flange  angles  j, 
and  the  connection  angles  d  are  placed  below  the  flange 
angles. 

With  this  kind  of  connection,  it  is  customary  to  assume 
that  the  rivets  in  the  connection  angles  transmit  the  entire 
135—15 


6  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


reaction  (end  shear  on  the  stringer)  to  the  floorbeam,  and  to 
ignore  the  supporting  effect  of  the  shelf  angles  and  stiff¬ 
eners;  the  shelf  angles  and  stiffeners,  however,  add  consider¬ 
ably  to  the  strength 
of  the  connections, 
and  should  always  be 
inserted  when  there 
is  room  for  them 
under  the  stringers. 


6.  In  Design  of 
a  Highw ay  Truss 
Bridge ,  Part  1,  it  was 
found  that  the  maxi¬ 
mum  end  shear  in  one 
of  the  roadway  string¬ 
ers  is  8,325  pounds. 
The  rivets  g,  Fig.  4, 
that  connect  the  an¬ 
gles  to  the  webs  of 


Fig.  4 


the  stringers  are  1  inch  in  diameter,  shop  driven,  in  double 
shear,  and  in  bearing  both  on  the  angles  and  on  the  web  of 
the  I  beam,  which  has  a  thickness  of  .45  inch  (Table  XIV). 
The  bearing  value  of  the  web  is  the  smallest;  as  the  rivets 
are  t  inch  in  diameter  and  the  allowable  bearing  stress  is 
22,000  pounds  per  square  inch  ( B .  S.,  Art.  103),  the  value 
is  f  X  .45  X  22,000  =  7,425  pounds.  Then,  the  required 
number  of  rivets  is  8,325  7,425  =  1.1;  three  rivets  will  be 

used  to  connect  each  pair  of  connection  angles  to  the  end 
of  the  stringer  {B.  S .,  Art.  155). 

To  find  the  number  of  rivets  h  required  to  connect  the 
connection  angles  to  the  web  of  the  floorbeam,  two  cases 
must  be  considered.  These  rivets  are  field  driven,  and  in 
bearing  both  on  the  connection  angles  and  on  the  web  of 
the  floorbeam.  When  the  load  in  one  panel  is"considered, 
the  amount  of  stress  transmitted  to  the  floorbeam  is 
8,325  pounds,  and  the  rivets  are  in  single  shear.  The  values 
of  the  rivets  for  the  allowable  stresses  given  in  B.  S ., 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE 


7 


Art.  103,  are  given  in  Table  XXXIX.  The  value  in  single 
shear  is  the  smallest,  and  is  3,980  pounds.  Then,  the  required 
number  of  rivets  for  this  condition  is  8,325  -f-  3,980  =  2.1. 
When  the  load  in  two  adjacent  panels  is  considered,  the 
amount  of  stress  transmitted  to  the  floorbeam  is  2  X  8,325 
pounds  =  16,650  pounds,  and  the  rivets  are  in  double  shear. 
In  this  case,  however,  the  bearing  value  of  a  rivet  on  the 
f-inch  web  of  the  floorbeam  is  the  smallest  value,  and  is 
5,060  pounds.  Then,  the  required  number  of  rivets  in  this 
case  is  16,650  -f-  5,060  =  3.3.  The  next  larger  even  number 
will  be  used,  in  this  case  four. 

According  to  B.  S .,  Art.  126,  the  connection  angles 
cannot  be  smaller  than  3  in.  X  3  in.  X  tV  in.  If  a  leg  3  inches 
wide  is  placed  next  to  the  web  of  the  stringer,  it  will  be 
impossible  to  get  three  rivets  in  it  without  spacing  them  too 
close  together;  so  a  leg  5  inches  wide  will  be  used,  and  the 
connection  angles  will  be  made  5  in.  X  3  in.  X  h  in.  The 
shelf  angles  will  be  made  3  in.  X  3  in.  X  "re  in.,  and  the  stiff¬ 
eners  will  be  made  2i  in.  X  2i  in.  X  in.  These  are  usually 
put  in  according  to  the  judgment  of  the  designer,  and  not 
by  rule. 

7.  Connection  of  Stringers  Under  Railway  Track. 
The  stringers  marked  g  in  Fig.  1  are  connected  to  the  floor- 
beam  in  the  same  way  as  those  just  considered.  The  connec¬ 
tion  is  shown  in  Fig.  5,  in  which  ( a )  is  the  cross-section  of 
the  upper  part  of  the  floorbeam,  and  shows  the  elevation 
of  the  ends  of  two  stringers,  resting  on  shelf  angles  d,  d; 
(b)  is  a  cross-section  of  one  of  the  stringers  on  the 
section  cc ,  and  shows  the  elevation  of  a  part  of  the  floor- 
beam.  The  stringers  are  cut  back  at  e  to  clear  the  top  flange 
angles  of  the  floorbeam.  In  Design  of  a  Highway  Truss 
Bridge ,  Part  1,  it  was  found  that  the  maximum  end  shear 
in  the  stringer  g  is  21,610  pounds.  The  web  of  the  I  beam 
is  .46  inch  thick,  and  the  value  of  one  f-mch  rivet  that  con¬ 
nects  the  angles  to  the  stringer  is  .75  X  .46  X  22,000 
=  7,590  pounds.  The  required  number  of  rivets  is,  then, 
21,610  -j-  7,590  =  2.8,  or,  say,  3. 


8 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


To  determine  the  number  of  rivets  /  required  to  connect 
the  connection  angles  to  the  web  of  the  floorbeam,  two  cases 
must  be  considered.  These  rivets  are  field  driven,  and  in 
bearing  both  on  the  connection  angle  and  on  the  web  of 
the  floorbeam.  When  the  load  in  one  panel  is  considered, 
the  amount  of  stress  transmitted  to  the  floorbeam  is 
21,610  pounds,  and  the  rivets  are  in  single  shear  (value 
=  3,980  pounds).  The  required  number  of  rivets  for  this 
condition  is  21,610  -4-  3,980  =  5.4,  or,  say,  6.  When  the 
load  in  two  adjacent  panels  is  considered,  it  is  necessary  to 


compute  the  amount  of  load  that  is  transmitted  to  the  floor- 
beam.  This  is  found  in  the  same  way  as  in  Design  of  a 
Highway  Truss  Bridge ,  Part  1,  except  that,  since  stringer 
connections  are  under  consideration,  it  is  necessary  to  allow 
for  the  increase  due  to  the  overturning  effect  of  the  wind. 
The  amount  of  dead  load  is  3,600  pounds,  and  of  live  load 
15,384  pounds.  The  allowance  for  impact  and  vibration  is 
1-0“  X  15,384  =  4,615  pounds,  and  for  the  overturning  effect 
of  the  wind,  2,308  pounds.  Then,  the  total  load  is  25,907 
pounds.  The  value  of  a  rivet  in  bearing  on  the  f-inch  floor- 
beam  web  (5,060  pounds)  is  the  smallest;  and  the  required 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  9 


number  of  rivets  for  this  condition  is  25,907  -r  5,060  —  5.1, 
or,  say,  6,  as  before.  It  is  well,  when  possible,  to  add  one  or 
two  rivets  to  the  required  number  in  stringers  under  railway 
tracks,  and  to  use  good-sized  connection  angles.  For  this 
reason,  five  and  eight  rivets,  respectively,  will  be  used,  as 
shown  in  Fig.  5,  and  the  connection  angles  will  be  made 
32  in.  X  32  in.  X  2  in.,  which  is  slightly  larger  than  the 
smallest  allowable  connection  angle  (A.  S.,  Art.  126). 

8.  Connection  of  Center  Stringer. — The  same  .con¬ 
nection  will  be  used  for  the  stringer  marked  h,  Fig.  1,  as  for^, 
except  that  in  the  connection  angles  only  four  rivets  will  be 
driven  in  the  legs  that  are  in  contact  with  the  stringers,  and  six 
rivets  in  the  legs  that  are  in  contact  with  the  floorbeam  web. 

9.  Connection  of  Bracket  and  Floorbeam  to  Truss. 
The  connection  of  the  bracket  and  that  of  the  floorbeam  to 
the  truss  are  shown  in  Fig.  6,  in  which  (a)  is  an  elevation 
of  the  ends'  of  the  bracket  and  floorbeam  that  connect  to  the 
truss;  ( b )  is  a  cross-section  on  D  D;  and  (e)  is  a  top  view  of 
the  bracket  and  doorbeam.  The  floorbeam  is  connected  to 
one  side  of  the  vertical  post  EE,  and  the  bracket  to  the 
other.  When,  as  in  this  case,  the  vertical  post  consists 
of  two  channels,  a  diaphragm  /,  consisting  of  a  web  and 
two  angles  at  each  side,  is  riveted  between  the  channels. 
The  leg  of  the  angle  adjacent  to  the  web  of  the  diaphragm 
is  made  2 \  inches  wide;  the  other  is  made  the  same  width 
as  the  outstanding  leg  of  the  floorbeam  connection  angle. 

10.  The  end  shear  on  the  floorbeam  was  found  in  Design 
of  a  Highway  Truss  Bridge ,  Part  1,  to  be  54,450  pounds. 
The  value  of  one  of  the  rivets^  that  connect  the  connection 
angle  h  to  the  web  of  the  floorbeam  (f-inch  rivet,  shop  driven, 
in  bearing  on  f-inch  web)  is  6,190  pounds.  Then,  the  required 
number  is  54,450  -r-  6,190  =  8.8,  or,  say,  9.  The  value  of 
one  of  the  rivets  i  that  connect  the  angles  h  to  the  truss 
(f-inch  rivet,  field  driven,  in  single  shear)  is  3,980  pounds. 
Then,  the  required  number  is  54,450  -f-  3,980  =  13.7,  or,  say 
14.  In  the  leg  of  the  connection  angle  adjacent  to  the  web, 
ten  rivets  g  will  be  used;  in  the  other  leg,  a  rivet  i  will  be 


10 


Fig. 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  11 


placed  half  way  between  each  two  of  the  former,  making 
nine  rivets  in  each  of  the  outstanding  legs.  It  is  customary, 
as  in  this  case,  to  have  a  few  extra  rivets.  For  the  floorbeam 
connection  angles,  angles  3i  in.  X  3i  in.  X  i  in.  will  be  used. 

11.  The  shear  on  the  bracket  where  it  connects  to  the 

truss  is  16,240  pounds  ( Design  of  a  Highway  Truss  Bridge , 
Part  1).  The  number  of  rivets  required  in  the  leg  of  the 
angle  /  that  is  adjacent  to  the  web  of  the  bracket  is  3.1,  and 
in  the  outstanding  legs,  4.1.  The  rivets  in  these  connection 
angles,  which  will  be  made  3i  in.  X  3  in.  X  ■ft  in.,  will  be 
spaced  as  far  apart  as  allowable,  that  is,  6  inches  apart, 
thereby  bringing  seven  rivets  through  the  web  and  twelve 
through  the  vertical  post.  , 

12.  Connection  of  Bracket  to  Floorbeam. — To  assist 
in  making  the  bracket  and  floorbeam  act  as  a  single  beam, 
the  top  flanges  should  be  connected  to  each  other.  A  good 
method  of  connecting  them,  when  the  bracket  and  floorbeam 
are  attached  to  different  sides  of  a  vertical  post,  is  shown  in 
Fig.  6.  Two  angles  k ,  k ,  the  same  size  as  those  in  the  top 
flange  of  the  bracket,  are  placed  close  to  the  vertical  post,  one 
angle  on  each  side,  and  their  ends  are  connected  to  the  ends  of 
the  bracket  and  floorbeam  flange  angles  by  means  of  plates  /,  /. 

The  stress  transmitted  by  the  angles  k  is  found  by  divi¬ 
ding  the  greatest  negative  bending  moment  on  the  bracket 
by  the  depth  of  the  bracket  at  the  truss.  In  the  present 
case,  the  stress  is  802,800  -f-  42  =  19,100  pounds,  tension, 
and,  as  there  are  two  angles,  each  transmits  9,050  pounds. 
The  value  of  one  of  the  rivets  m  that  connect  the  end  of  an 
angle  k  to  the  plate  /,  Fig.  6  {c)  (f-inch  rivet,  field  driven,  in 
single  shear)  is  3,980  pounds;  then,  the  required  number  of 
rivets  is  9,050  4-  3,980  =  2.3,  or,  say,  3.  The  same  number 
is  used  to  connect  the  other  ends  of  the  angles  and  to  connect 
the  plates  to  the  top  flanges  at  n  and  o. 

The  required  thickness  t  of  the  plate  /  is  given,  approxi¬ 
mately,  by  the  formula 

4  Sd 
~  sw' 


\ 


\ 


12  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  8  78 


in  which  A  =  stress  transmitted  by  one  angle  k ; 

d  =  width  of  widest  vertical  member  to  which 
floorbeams  are  connected— that  is,  the  clear 
distance  between  the  angles  k\ 
s  =  working  stress  in  bending; 
w  =  width  of  plate  /,  measured  along  bracket. 

The  width  w  is  controlled  by  the  rivet  spacing  in  the  plate; 
in  the  present  case,  it  is  8  inches.  Then, 


4  X  9,050  X  10 
~  16,000  X  8 2 


.354,  or,  say,  f  inch 


The  angles  k  and  plates  /  are  frequently  omitted,  and  the 
rivets  p  that  connect  the  bracket  to  the  vertical  post  are 
depended  on  to  transmit  the  stress  in  the  bracket.  This 
construction  is  not  recommended,  as  it  tends  to  overstrain 
the  rivets  and  allow  the  brackets  to  sag  at  the  ends. 

The  bottom  flanges  of  the  bracket  and  floorbeam  are  not 
connected,  but  are  made  to  bear  against  the  outsides  of  the 
vertical  posts,  the  stress  being  transmitted  from  one  to  the 
other  by  means  of  angles  r  that  are  riveted  to  the  bottom  of 
the  diaphragm. 


13.  Connection  of  End  Floorbeam  to  Truss. — As 
there  is  no  vertical  member  at  the  end  joint,  the  end  floor- 
beam  cannot  be  connected  to  the  truss  in  the  same  way  as 
the  other  floorbeams.  It  will  be  supported  on  a  chair  riveted 
to  the  end  post.  The  detail  of  the  chair  will  be  treated  later, 
in  connection  with  the  design  of  the  pin  at  the  joint  a.  The 
portion  of  the  end  floorbeam  directly  over  the  truss  is  shown 
in  Fig.  7,  in  which  ( a )  is  the  elevation  and  ( b )  the  cross-sec¬ 
tion  of  the  floorbeam;  the  latter  view  shows  also  the  relative 
location  of  floorbeam,  end  post,  and  bottom  chord.  In  order 
that  the  bottom  flange  angles  of  the  floorbeam  shall  not 
interfere  with  the  top  flange  angles  of  the  end  post  at  e ,  it 
is  necessary  to  place  the  bottom  of  the  floorbeam  1  foot 
8  inches  above  the  center  line  of  the  bottom  chord,  making 
the  floorbeam  8  inches  shallower  than  the  intermediate  floor- 
beams,  that  is,  34i  inches,  as  assumed  in  Design  of  a  High¬ 
way  Truss  Bridge ,  Part  1. 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  13 


Bottom  Chore/ 


14  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


The  web  of  the  bracket  and  floorbeam  is  in  one  piece 
extending  the  full  length.  Plates  c  having  the  same  area  as 
the  flange  angles  of  the  bracket  are  riveted  to  the  top  and 
bottom  flanges  to  splice  the  bracket  flange  angles  to  the 
floorbeam  flange  angles.  Stiffeners  d  are  riveted  to  the  web 
where  the  beam  rests  on  the  chair  at  the  truss.  The  stringers 
are  connected  to  the  end  floorbeam  and  brackets  in  the  same 
way  as  to  the  other  floorbeams  and  brackets,  except  that  there 
is  a  shelf  angle  and  stiffener  on  but  one  side  of  the  web. 


SPLICES 


14.  The  only  splices  that  are  necessary  are  in  the  top 
chord.  In  Design  of  a  Highway  Truss  Bridge ,  Part  1,  it  was 
decided  that  the  splices  would  be  located  in  the  panels  CD 
and  D'  C'  close  to  the  joints  D  and  D\  respectively.  The 
form  of  cross-section  used  for  the  member  CD  is  shown  in 
Fig.  27  of  the  Section  just  referred  to.  This  member  will  be 


f 

J  SI 


Q 

- — - S - ■ - 1  ^ 

•  •  •  j  Q  G  Q 

G 

O 

o 

G 

— 

• 

• 

G 

G 

•  •  •  !  G  G  Q 

°\ 

Q 

•  •  ]  G  G 

G 

Q 

•  •  •  |  G   O  G 

G 

VssS'  vsrJ'  VSSS'  \ 

c 


(a) 

Fig.  8 


spliced  by  means  of  four  bars  3i  inches  wide  riveted  to  the 
outstanding  legs  of  the  flange  angles,  and  by  vertical  splice 
plates  inside  and  outside  of  the  section,  as  shown  in  Fig.  8. 
The  following  splice  plates  will  be  used: 

Square 

Inches 

Four  plates  3^  in.  X  A  in.,  gross  area  =  6.1  2  5 

Two  plates  15  in.  X  A  in.,  gross  area  =  9.3  7  5 

Two  plates  14  in.  X  Ain.,  gross  area  =  8.7  5 


Total  gross  area  =  2  4.2  5  0 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  15 


This  section  is  slightly  less  than  that  of  CD,  blit,  as  it  is 
so  little  less,  and  as  it  is  greater  than  the  required  area  found 
for  CD ,  these  splice  plates  will  be  used.  The  rivets  in  the 
splice  will  be  made  i  inch  in  diameter.  Each  splice  plate 
must  have  sufficient  rivets  on  each  side  of  the  splice  to 
transmit  its  stress  to  and  from  the  ends  of  the  members. 

It  is  customary  to  rivet  the  splice  plates  to  the  end  of  one 
member  in  the  shop,  and  connect  the  other  end  in  the  field. 
The  required  number  of  field  rivets  in  a  splice  plate  is  found 
by  dividing  the  product  of  the  area  of  the  plate  and  the  work¬ 
ing  stress  by  the  value  of  one  rivet.  In  the  present  case,  the 
working  stress  in  CD,  as  found  in  Part  1,  is  14,290  pounds 
per  square  inch.  The  smallest  value  of  a  rivet  in  this  case 
is  its  value  in  single  shear,  or  5,410  pounds.  Then,, the 
number  of  field  rivets  required  to  connect  each  splice  plate 
is  as  follows: 

~  i  *  oi  •  v/  7  •  1.531  X  14,290  a  nz  '  a 

One  plate  S f  in.  X  tg  in., - „  J<t  » . —  =  4.05,  or,  say,  4 

0,410 

1  ,  v.  5  •  '4.687  X  14,290  10  . 

One  plate  lo  in.  X  tg  m., - - - — 2 -  =  12.4,  or,  say,  13 

5,410 

One  plate  14  in.  X  tg  in., - _  i  ’ -  =  11. 0,  or,  say,  12 

5,410 

As  the  value  of  a  shop-driven  rivet  is  greater  than  that  of 
afield-driven  rivet  (B.  S.,  Art.  103),  fewer  shop-driven  rivets 
are  required,  but  it  is  customary  to  place  the  same  number  of 
rivets  on  each  side  of  the  joint. 

15.  The  splice  is  shown  in  Fig.  8,  in  which  (a)  is  an  eleva¬ 
tion  and  (/)  a  cross-section  of  the  top  chord.  The  3i-inch 
splice  plates  are  marked  c,  the  15-inch  splice  plates  are 
marked  d ,  and  the  14-inch  splice  plates  are  marked  e.  The 
dotted  line  //  is  the  joint;  the  ends  of  the  sections  of- chord 
are  planed  smooth  on  the  line  //so  that  the  ends  will  bear 
against  each  other  and  so  transmit  some  of  the  stress.  Some 
engineers  depend  on  this  bearing  to  transmit  the  entire  stress 
in  compression  members,  putting  just  enough  rivets  in  the 
splice  plates  to  hold  the  members  in  line.  This  is  not  the  best 
practice;  each  splice,  whether  in  tension  or  in  compression, 


16  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


should  be  designed  as  stated,  and  sufficient  section  pro¬ 
vided  in  the  splice  plates  and  sufficient  rivets  to  fully  transmit 
the  stress.  In  some  cases,  tie-plates  are  made  to  serve  as 
splice  plates,  instead  of  the  3i-inch  plates  on  the  outstanding 
legs  of  the  flange  angles.  In  this  case,  the  whole  width  of 
tie-plates  should  not  be  counted  as  splice  plates,  but  only  that 
portion  in  contact  with  and  close  to  the  outstanding  legs  of 
the  flange  angles.  ’  _ _ 

DESIGN  OF  FINS  AND  PIN  PLATES 

16.  Bending  Moment  on  Pins. — In  Bridge  Members 
and  Details ,  Part  2,  it  was  stated  that  pins  are  designed  to 
resist  the  greatest  bending  moment  to  which  they  are  sub¬ 
jected.  The  bending  moments  on  the  pins  are  found  from 
the  stresses  in  the  members  that  connect  to  the  pins.  In 
order  to  find  the  maximum  bending  moment  on  a  pin,  it  is 
customary  to  compute  the  moment  for  several  conditions  of 
loading;  for  example,  it  may  first  be  computed  when  the 
stresses  in  the  web  members  that  connect  to  the  pin  are 
greatest,  that  is,  when  there  is  a  partial  live  load  on  the 
truss;  and  then  computed  when  the  stresses  in  the  chord 
members  that  connect  to  the  pin  are  greatest,  that  is,  when 
there  is  a  full  live  load  on  the  truss.  For  each  of  these 
cases  it  is  necessary  to  calculate  the  stresses  that  occur 
simultaneously  in  the  other  members;  for  example,  when  the 
chord  stresses  are  greatest,  it  is  necessary  to  compute  the 
stresses  that  obtain  in  the  web  members  when  there  is  a  full 
live  load  on  the  truss,  and  to  use  these  stresses  in  finding 
the  bending  moment  on  the  pin  for  that  loading.  Similarly, 
when  the  maximum  stresses  in  the  web  members  are  con¬ 
sidered,  it  is  necessary  to  compute  the  stresses  in  the  chord 
members  for  the  loading  that  causes  the  greatest  stresses  in 
the  web  members. 

In  finding  the  forces  that  act  on  a  pin,  it  is  usually  assumed 
that  the  stress  in  each  member  is  evenly  distributed  among 
the  several  portions  of- the  member  bearing  on  the  pin,  and 
that  the  stress  in  each  portion  acts  as  a  concentrated  load  at 
its  center  of  bearing. 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  17 


17.  In  finding  the  bending  moment  on  a  pin,  it  is  con¬ 
venient  to  resolve  the  forces  that  act  on  the  pin  into  their 
vertical  and  horizontal  components,  and  then  to  find,  at  the 
section  where  the  moment  is  desired,  the  bending  moments 
My  and  MH,  due  to  the  vertical  and  to  the  horizontal  forces, 
respectively.  The  resultant  bending  moment  M  on  the  pin 
at  any  section  is  then  found  by  means  of  the  formula 

M  =  VM-’  +  M„' 

When  the  largest  value  of  M  has  been  determined,  the  pin 
having  a  resisting  moment  as  great  as  M  is  found  from 
Table  XLI.  How  the  details  of  this  process  are  worked  out 
will  be  explained  presently. 

Many  designers  find  the  largest  pin  required  and  make  the 
others  the  same  size.  This  simplifies  the  work  in  the  shop 
somewhat,  but  there  is  no  other  reason  for  doing  it. 

The  bending  moments  can  be  found  by  the  graphic  as  well 
as  by  the  analytic  method.  Whichever  method  is  used,  it  is 
necessary  to  thoroughly  understand  the  steps  that  are  taken 
before  the  bending  moment  can  be  found.  These  steps  can 
best  be  explained  and  illustrated  in  connection  with  the 
analytic  method.  For  this  reason,  the  bending  moments  on 
the  pins  discussed  in  the  following  pages  are  found  by  means 
of  the  analytic  method.  They  can  also  be  found  by  the 
graphic  method  by  applying  the  principles  explained  and 
illustrated  in  Graphic  Statics. 

18.  Width  of  Top  Chord. — Before  designing  the  pins, 
it  is  necessary  to  decide  definitely  on  the  distance  between 


the  webs  of  the  top  chord.  In  Design  of  a  Highway  Trass 
Bridge ,  Part  1,  this  was  assumed  as  12  inches,  but  no 


18  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 

calculation  was  made  to  verify  the  assumption.  In  a  bridge 
of  this  kind,  it  is  best  to  consider  first  the  second  joint  of  the 
top  chord,  in  this  case  joint  C,  Fig.  9.  The  arrangement  of 
the  members  at  C  is  shown  in  Fig.  10",  in  which  (a)  is  the 
elevation  of  the  joint,  and  ( b )  is  a  cross-section  of  the  top 
chord  showing  the  relative  positions  of  the  vertical  Cc  and 
the^diagonal  Cd. 

The  width  of  the  vertical  has  been  taken  as  8i  inches 
(Part  1).  If  pin  plates  are  required,  they  will  be  placed  on 
the  insides  of  the  channels,  as  shown  at  e ,  Fig.  10,  and  the 
heads  of  the  rivets  that  connect  them  to  the  channels  will  be 
flattened  to  a  height  of  f  inch  on  the  outside  of  the  channel. 
This  makes  the  vertical  8i  +  f  +  s  =  9i  inches  wide  over 
the  rivet  heads.  The  eyebars  /,  /  that  form  the  diagonal  C d 
are  placed  outside  the  vertical,  and  as  close  to  it  as  possible. 
It  is  customary  to  allow  tV  inch  between  the  eyebars  and 
other  members  or  rivets  heads,  so  in  this  case  their  inner 
surfaces  will  be  9f  inches  apart;  and  since  they  are  i  inch  in 
thickness,  their  outer  surfaces  will  be  9f  -f-  f  +  i  =  11  &  inches 
apart.  Allowing  tV  inch  on  each  side  for  clearance,  and 
f  inch  for  the  height  of  the  flattened  rivet  heads  on  the 
inside  of  the  chord,  gives  Hi  +  iV  +  iV  +  f  +  f  =  12  inches 
for  the  distance  between  the  webs  of  the  chord,  as  shown  in 
Fig.  10  {b). 

In  the  following  pages,  the  pins  and  pin  plates  will  be 
designed.  In  the  first  joint,  the  diameter  of  the  pin  will  be 
assumed  at  random,  and  the  required  diameter  found  by  the 
usual  method,  that  is,  by  successive  trials.  The  same  gen¬ 
eral  method  is  used  in  practice  for  all  the  other  joints;  but 
in  order  to  economize  space  in  this  Section,  the  diameter  of 
each  pin  as  obtained  after  several  trials  will  be  given  at  once, 
and  this  value  will  then  be  verified. 

« 

19.  Pins  and  Pin  Plates  at  Joint  C. — The  stresses 
in  the  members  that  meet  at  C  are  shown  in  Fig.  11.  They 
are  the  maximum  stresses  in  these  members,  and  are  not 
simultaneous ;  that  is,  the  stress  in  the  diagonal  Cd  is  not  a 
maximum  when  those  in  the  chord  members  are  greatest, 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  19 


01  ‘Old 


20  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


and  vice  versa.  In  the  design  of  top-chord  pins,  however,  it 
is  customary  to  ignore  the  maximum  stresses  in  the  chord 
members,  as  a  part  of  the  stress  is  transmitted  from  one 
panel  to  the  next  without  passing  through  the  pin.  It  is 
simply  necessary  to  ascertain  in  each  case  the  greatest 
amount  of  stress  transmitted  to  the  chord  at  the  joint;  in  the 
present  case,  this  is  equal  to  the  horizontal  component  of  the 
stress  in  Cd ,  and  is  found  by  multiplying  the  maximum 
stress  in  Cd  by  cos  H\  in  this  case,  it  is  139,000  X  .595 

* 

=  82,700.  Then,  the  maximum  stress  in  the  vertical  being 
known,  the  maximum  forces  acting  on  the  pin  are  as  shown 


B  +272/00  C  +340/00  T>  4  362800  E 


in  Fig.  10  {e) .  The  dead  panel  load  of  4,765  pounds  is  dis¬ 
tributed  over  the  pin  by  various  members,  but  will  for 
convenience  be  assumed  to  be  applied  at  the  centers  of  the 
eyebars. 

The  diameter  of  the  pin  will  be  assumed  to  be  4  inches. 
Then,  since  the  total  stress  in  the  vertical  is  116,500  pounds, 
and  the  working  stress  in  bearing  on  the  pin  is  22,000  pounds 
per  square  inch,  the  required  thickness  of  bearing  for  Cc  is 

116,500 


4  X  22,000 


—  1.324  inches 


The  web  of  a  10-inch  20-pound  channel  (member  Cc)  is 
.38  inch  thick,  so  that  the  thickness  to  be  made  up  by 
pin  plates  is  1.32  —  2  X  .38  =  .56  inch,  or  .28  inch  on  each 
channel.  Two  pin  plates  e,  e,  Fig.  10  («)  and  (b) ,  -re  inch 
thick,  will  be  used.  Then,  the  thickness  of  bearing  for  each 
channel  will  be  .38  4  .31  =  .69  inch,  the  center  of  which  is 
.69  -i-  2  =  .345  inch  from  the  back  of  the  channel.  The 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  21 


centers  of  bearings  for  the  two  sides  of  the  vertical  member 
are,  then,  8.5  —  .345  —  .345  =  7.81  inches  apart,  as  shown  at 
h  and  h'  in  Fig.  10  (c) . 

The  required  thickness  of  bearing  of  the  top  chord  is 


82,700 
4  X  22,000 


=  .94  inch 


or  .94  -f-  2  =  .47  inch  on  each  side.  If  the  8"  X  tV'  side 
plates  that  form  part  of  the  member  CD  are  continued  a 
short  distance  beyond  C,  as  shown  at  g,  Fig.  10  («),  the 
thickness  of  bearing  on  each  side  will  be'  f  inch,  which  is 
sufficient,  and  the  centers  of  bearing  for  the  two  sides  of  the 
chord  will  be  12  +  .3125  -f  .3125  =  12.625  inches  apart,  as 
shown  in  Fig.  10  (d). 

As  the  eyebars  are  9f  inches  apart  and  1  inch  thick,  the 
distance  between  their  centers  is  10i  inches,  as  shown  in 
Fig.  10  (c)  and  (d). 

Assuming  that  the  stress  in  each  half  of  a  member  acts  as 
a  concentrated  load  at  its  center  of  bearing,  the  horizontal 
forces  that  act  on  the  pin  at  C  are  shown  in  Fig.  10  (d)  and 
the  vertical  forces  in  Fig.  10  (c). 

It  will  be  observed  that  the  bending  moment  at  any  point 
between  h  and  h! ,  Fig.  10  {c) ,  is  equal  to  the  moment  of  the 
couple  formed  by  the  two  equal  forces  at  either  end  of  the 
pin.  The  lever  arm  of  this  couple  is 

i  X  (10.25  -  7.81)  =  2.44  -s-  2  =  1.22  inches 

The  moment  is,  therefore, 

58,250  X  1.22  =  71,065  inch-pounds  ( ==  My) 

It  is  evident  that  the  moment  at  the  left  of  h  or  at  the 
right  of  h'  is  less  than  this. 

Similarly,  the  bending  moment  at  any  point  between  g 
and^',  Fig.  10  (d) ,  is 

41,350  X  --  —  =  49,100  inch-pounds  (=  MH) 

& 


For  the  resultant  moment  we  have,  therefore, 

M  —  V71,065*  +  49,1002  =  86,400  inch-pounds 
Consulting  Table  XLI,  since  the  working  stress  in  bend¬ 
ing  on  the  pin  is  22,000  pounds  per  square  inch,  it  is  seen 
that  a  pin  3a  inches  in  diameter  is  the  smallest  that  has 

135—16 


22  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


the  required  value  of  resisting-  moment.  The  various  steps 
will  now  be  repeated,  using  3i  inches  for  the  diameter  of 
the  pin. 

The  required  thickness  of  bearing  for  the  vertical  is  now 

116,500 


3.5  X  22,000 


—  1.513  inches 


Two  |-inch  pin  plates  will  be  used,  making  the  thickness 
of  bearing  on  each  side  .38  +  .38  =  .76  inch,  and  the  distance 
between  the  centers  of  bearings  7.74  inches,  as  shown  in 

Fig.  12.  The  bending 
moment  due  to  the  verti¬ 
cal  forces  is  'now  58,250 
X  1.255  -  73,100  inch- 
pounds;  that  due  to  the 
horizontal  forces  re¬ 
mains  the  same  as  be¬ 
fore,  since  the  thickness  of  bearing  of  top  chord  used  before 
is  sufficient.  Then,  the  corrected  value  of  the  maximum 
bending  moment  on  the  pin  is 

V^OTOO1  +  73,1002  —  88,100  inch-pounds 


A  pin  Sk  inches  in  diameter  has  a  sufficient  resisting 
moment,  and  will  be  used. 


20.  The  total  width  or  thickness  of  bearing  on  each  side 
of  the  vertical  Cc,  Fig.  10,  is  .76  inch.  If  the  stress  is 
assumed  to  be  evenly  distributed  over  this  width,  then, 
since  the  thickness  of  the  pin  plate  is  t  inch,  the  amount  of 
stress  transmitted  by  each  plate  is 

X  58,250  =  29,125  pounds 

The  rivets  that  connect  the  pin  plates  to  the  channel  are 
i  inch  in  diameter  and  shop  driven;  the  value  in  single  shear, 
4,860  pounds,  is  the  smaller.  The  number  of  rivets  required 
to  transmit  the  stress  in  the  pin  plate  to  the  channel  is, 
therefore,  29,125  -=-  4,860  =  6.  In  addition  to  the  required 
number,  which  will  be  placed  below  the  pin,  it  is  customary 
to  put  a  few  rivets  above  the  pin  to  hold  the  pin  plates  firmly 
to  the  web  of  the  channel,  as  shown  in  Fig.  13.  Since  the 


i 


§78  DESIGN  OP  A  HIGHWAY  TRUSS  BRIDGE  23 


distance  c  (Table  XIII)  for  a  10-inch  20-pound  channel  is 
8i  inches,  the  pin  plates  will  be  made  8  inches  wide. 

The  section  of  the  top  chord  is  decreased  in  area  by  the 
pinhole,  but  in  this  case  this 
is  more  than  made  up  by  the 
8-inch  plates  on  the  sides. 

21.  Pins  and  Pin  Plates 
at  Joints  D  and  E. — The 
required  sizes  of  the  pins  at 
D  and  E,  Fig.  9,  can  be  found 
by  proceeding  in  the  same 
way  as  for  joint  C.  In  the 
present  case,  and  almost  in¬ 
variably  in  the  kind  of  truss  under  consideration,  they  both 
work  out  smaller  than  that  required  at  C,  but  for  the  sake  of 
uniformity  they  are  made  the  same  size  as  at  C.  Pin  plates  a , 
Fig.  14,  7  in.  X  A  in.,  with  four  rivets  below  and  two  above 
the  pinhole  will  be  riveted  to  the  insides  of  the  channels  of 
D  d  and  E e\  no  pin  plates  are  required  on  Ee ,  but  it  is  cus¬ 
tomary  in  the  best  practice  to  provide  at  least  one  plate. 

The  upper  chord  is  decreased  in  section  by  the  pinholes 
at  D  and  E\  to  restore  the  lost  section,  vertical  plates  a , 
Fig.  15,  will  be  riveted  to  the  insides  of  the  webs.  As 


iio  ©i 

io  oii 

!!  O  1 

;  O  i 

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!  \  ©  / 
t  \ _ / 

i 

i 

t 

i 

L  of  1 

1 

1 

1 

1 

1 

« -  -  _  1 

Fig.  13 

Fig.  14 

!  Q 

i 

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© 

© 

© 

1  ©  !  O  © 

© 

© 

© 

!© 

/  i 

© 

o 

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. 

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i 

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© 

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L 

i 

Fig.  15 


the  thickness  of  metal  at  D  and  E  through  which  the  pin 
passes  is  f  inch  on  each  side  of  the  chord,  the  lost  section  is 
X  f  =  2.625  square  inches/  A  plate  14  in.  X  f  in.  will  be 
added  on  each  side;  the  net  width,  deducting  the  diameter 
of  the  pinhole,  is  '10i  inches,  and  the  area  is  3.94  square 


24  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


inches.  This  is  more  than  is  necessary,  but  the  plate  is  made 
thicker  than  required,  on  account  of  the  fact  that  at  D  the 
rivets  connecting  the  plate  to  the  web  will  have  to  be 
countersunk  on  the  inside,  to  make  room  for  the  eyebars 
composing  De,  and  that  the  depth  of  a  countersunk  head  of 
a  |-inch  rivet  is  f  inch  (Table  XIX).  Hence,  thinner  plate 
cannot  be  used. 

The  working  stress  in  D  E  is  14,170  pounds  per  square 
inch  (see  Design  of  a  Highway  Truss  Bridge ,  Part  1);  and, 
since  the  section  is  decreased  2.625  square  inches  on  each 
side,  the  amount  of  stress  that  must  be  transmitted  by 
each  of  these  reinforcing  plates  is  2.625  X  14,170  =  37,200 
pounds.  The  rivets  that  connect  these  plates  to  the  web  of 
the  chord  are  f  inch  in  diameter  and  shop  driven;  the  value 
in  single  shear,  4,860  pounds,  is  the  smaller.  The  number 
of  rivets  required  in  each  plate  on  each  side  of  the  pin  is, 
then,  37,200  -r-  4,860  =  7.7,  or,  say,  8.  The  countersunk 
rivets  in  these  plates  are  not  considered  as  transmitting 
any  stress  (B.S.,  Art.  109). 


268000 

*r 


22.  Pin  and  Pin  Plates  at  Joint  B. — The  stresses  in 
the  members  that  meet  at  B  are  shown  in  Fig.  11.  They  are 
the  maximum  stresses,  and  are  not  simultaneous;  the  stress 

in  B  b  is  greatest  when  there  is  a  full 
panel  load  at  b ,  those  in  a  B  and  B  C 
are  greatest  when  the  truss  is  fully 
loaded,  and  that  in  Be  is  greatest 
when  the  joints  from  c  to  the  right 
are  loaded.  It  is  customary,  in  the 
design  of  the  pin  at  the  hip  joint  B , 
to  assume  that  the  stresses  in  a  B 
and  B  b  are  maximum  at  the  same 
time,  and  then,  using  the  stresses  in 
these  members  shown  in  Fig.  11,  to  find  by  the  method  of 
joints  the  simultaneous  stresses  in  B  C  and  Be,  using  the 
equations  2l  X  —  0  and  2'  Y  =  0.  On  this  assumption,  the 
simultaneous  forces  that  act  on  the  pin  are  shown  in  Fig.  16; 
it  is  unnecessary  to  consider  the  dead  panel  load  at  B. 


Fig.  16 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  25 


The  customary  arrangement  of  members  at  joint  B  is 
shown  in  Fig.  17,  in  which  (a)  is  the  elevation  of  the  joint; 
( b )  is  the  cross-section  of  the  top  chord  and  side  elevation  of 
the  pin,  showing  the  arrangement  of  members;  and  {c)  and 
( d )  are  half  top  views  and  half  bottom  views  of  the  top 
chord  and  end  post,  respectively.  The  top  chord  and  end 
posts  are  cut  off  on  the  line  ee,  leaving  about  i  inch  clear¬ 
ance  between  them;  the  flange  angles  and  webs  of  the  two 
members  are  almost  the  same  distance  from  the  center  of 
the  truss,  and  the  members  bear  against  opposite  sides 
of  the  pin.  Pin  plates  /  are  riveted  to  the  inside  of  the  end 
post  and  extend  beyond  the  pin  up  into  the  top  chord;  pin 
plates  g  are  riveted  to  the  outside  of  the  top  chord,  and 
extend  beyond  the  pin,  enclosing  the  end  of  the  end  post. 
The  eyebars  b,  b  that  form  the  diagonal  Be  are  placed  inside 
the  chord  and  the  end  post,  as  close  as  possible  to  the 
inside  pin  plates  /  of  the  end  post,  the  rivets  in  this  plate 
being  countersunk  on  the  inside  of  the  plate  to  allow  the 
eyebar  to  get  close  to  it.  The  hip  vertical  i  is  attached  to 
the  pin  by  means  of  hanger  plates  /,/  that  are  as  close  as 
possible  to  the  inside  of  the  eyebars.  The  plates  k  and  /  are 
tie-plates;  the  adjacent  ends  of  the  top  tie-plates  are  covered 
by  the  bent  plate  m  that  is  riveted  to  the  end  of  the  top 
chord.  The  two  angles  shown  in  cross-section  at  n  are  the 
top  flange  angles  of  the  portal;  it  is  customary  to  place  them 
above  and  to  continue  them  across  the  top  chord,  as  shown, 
connecting  them  to  it  by  means  of  the  bent  plates  o  and  p. 

23.  In  the  discussion  of  joint  C,  the  clear  distance 
between  the  webs  of  the  top  chord  was  found  to  be  12  inches; 
it  is  customary  to  have  the  distance  at  B  the  same.  Since 
the  webs  are  Te  inch  thick,  the  distance  between  the  vertical 
legs  of  the  flange  angles  is  12f  inches.  The  flange  angles 
of  the  end  post  will  also  be  placed  12f  inches  apart.  Since 
the  webs  of  the  end  post  are  tV  inch  thick,  the  clear  distance 
between  them  will  be  Ilf  inches. 

The  required  diameter  of  the  pin,  found  by  trial,  is 
4f  inches.  This  value  will  now  be  verified.  The  maximum 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  27 


stress  in  aB  and  B  C  being-  272,100  pounds,  and  the  working 
stress  in  bearing  22,000  pounds  per  square  inch,  the  required 
thickness  of  bearing  for  each  of  these  members  is 

272,100 


4.75  X  22,000 


—  2.6  inches, 


or  1.3  inches  on  each  side  of  the  member. 

The  webs  of  the  end  posts  are  tV  inch  thick,  and  the  side 
plates  2  inch  thick.  Pin  plates  /, /,  Fig.  17,  |  inch  thick, 
will  be  riveted  to  the  inside,  making  a  total  thickness  of 
Tre  inches  bearing  on  each  side.  As  the  clear  distance 
between  the  webs  is  Ilf  inches,  the  clear  distance  between 
the  plates  /  is  11  inches,  and  the  distance  between  the  cen¬ 
ters  of  the  bearings  is  12ts  inches.  Since  the  pin  plates  are 
f  inch  thick,  and  the  total  width  of  bearing  on  each  side  is 
lxe  inches,  the  amount  of  stress  transmitted  by  one  pin  plate  is 

— 1---—  X  136,050  =  38,900  pounds, 

1.3125 


and  the  number  of  rivets  required  to  connect  the  plate  to  the 
end  post  is  38,900  -r-  4,860  =  8. 

The  webs  of  the  top  chord  are  re  inch  thick.  Pin  plates  y, 
8  in.  X  t  in.,  will  be  placed  on  the  outside  of  the  member 
between  the  vertical  legs  of  the  flange  angles;  pin  plates  r, 
14  in.  X  i  in.,  will  be  placed  outside  of  the  vertical  legs  of 
the  angles  and  the  plates  q\  and  pin  plates  g ,  14  in.  X  I  in., 
will  be  placed  outside  of  the  plates  r  and  enclosing  the  end 
of  the  end  post.  This  makes  the  total  thickness  of  bearing 
at  each  side  li^e  inches,  and  the  distance  between  the  centers 
of  bearings,  131^6  inches.  The  numbers  of  rivets  required  to 
connect  these  plates  to  the  top  chord  are: 


Plate,  14  in.,  X  t  in., 


Plate,  14  in.,  X  i  in., 


.375 

1.3125 


X  136,050 


.25 


1.3125 


4,860 
X  136,050 


4,130 


=  8  rivets 


=  6.3,  or,  say,  7  rivets 


.375 

1.3125 


X  136,050 


8  rivets 


Plate,  8  in.  X  f  in., 


4,860 


28  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


In  Fig.  17  (a),  there  are  ten  rivets  (not  counting  counter¬ 
sunk  rivets)  in  the  right-hand  end  of  plate  g,  five  rivets  in 
the  plate  r  beyond  the  end  of  g,  and  eight  rivets  in  the  plate  q 
beyond  the  end  of  plate  r.  This  is  the  customary  way  of 
arranging  the  rivets  when  more  than  one  pin  plate  is  used. 

24.  The  clear  distance  between  the  pin  plates  /  on  the 
end  post  was  found  to  be  11  inches;  leaving  t&  inch  clearance 
on  each  side  makes  the  outside  surfaces  of  the  eyebars 
!0i  inches  apart,  their  centers  being  101  —  li  =  9f  inches 
apart,  and  their  inside  surfaces  10l  —  li  —  li  =  8f  inches 
apart.  Leaving  tV  inch  clearance  on  each  side  makes  the 
outside  surfaces  of  the  hanger  plates  j  of  the  hip  vertical 
81  inches  apart,  as  shown  at  the  top  of  Fig.  17  ( b ).  It  is 
customary  to  make  the  hanger  plates  not  less  than.f  inch 
thick,  although  in  many  cases  thinner  plates  give  sufficient 
bearing  on  the  pin.  A  plate  t  inch  thick  will  be  used  in  the 
present  case.  No  calculation  will  be  made  for  the  required 
thickness  of  bearing,  as  the  actual  thickness  is  greater  than 
necessary;  the  required  net  section  of  the  hanger  plates, 
however,  must  be  computed. 

In  Design  of  a  Highway  Truss  Bridge ,  Part  1,  the  required 
net  section  of  B  b  was  found  to  be  4.7  square  inches.  In 
B.  S.,  Art.  143,  it  is  specified  that  riveted  tension  members 
shall  have  a  net  section  through  the  pinhole  25  per  cent, 
greater  than  the  net  section  of  the  member.  Since  the 
required  net  section  of  B  b  is  4.7  square  inches,  the  required 
net  section  of  the  hanger  plates  through  the  pinholes  is 
1.25  X  4.7  =  5.88  square  inches.  As  there  are  two  plates, 
each  plate  must  have  a  net  section  equal  to  5.88  -f-  2 
=  2.94  square  inches.  Hanger  plates  10  in.  X  t  in.  will  be 
used;  the  net  width  (deducting  the  diameter  of  the  pin)  is 
10  —  41  =  5i  inches,  and  the  net  area  is  5i  X  i  =  3.28  square 
inches,  which  is  sufficient.  The  rivets  that  connect  the 
hanger  plates  to  Bb  are  f  inch  in  diameter,  shop  driven,  and 
in  single  shear;  their  value  is  4,860  pounds.  Then,  since 
the  stress  in  Bb  is  75,500  pounds,  the  number  of  rivets 
required  to  connect  each  plate  is  37,750  -7-  4,860  =  7.8,  or. 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  29 


say,  8.  In  Fig.  17  (b) ,  the  distance  between  the  outer  sur¬ 
faces  of  the  hanger  plates  is  shown  as  8i  inches;  then,  the 
distance  between  centers  of  bearings  is  8i  —  i  =  7i  inches. 

25.  The  horizontal  forces  acting  on  the  pin  are  shown 
in  Fig.  18  (a),  and  the  vertical  forces  in  Fig.  18  (b).  The 
greatest  moment  due  to  the  horizontal  forces  is  between 


\ 


Fig.  18 


c  and  c',  and  is  constant;  it  is  equal  to  the  moment,  about  c , 
of  the  forces  on  the  left  of  c ,  or 

134,000  X  1.781  -  81,000  X  1.281  -  134,900  inch-pounds 
The  greatest  moment  due  to  the  vertical  forces  is  between 
d  and  d'\  it  is  constant  between  these  two  points,  and  is 
equal  to  the  moment,  about  d,  of  the  forces  on  the  left  of  d,  or 
109,300  X  2.219  —  71,600  X  .9375  =  175,400  inch-pounds 
Then,  the  greatest  bending  moment  on  the  pin  is  from 
d  to  d',  and  its  value  is 

Vl34,9002  +  175, 4002  =  221,300  inch-pounds 
Consulting  Table  XLI,  it  is  seen  that  a  4f-inch  pin  has 
sufficient  resisting  moment. 

26.  Packing  of  Bottom  Chord. — The  process  of 
arranging  the  members  on  the  bottom-chord  pins  is  spoken 


30  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


of  as  packing  the  bottom  chord,  and  the  arrangement  is 
called  the  bottom-chord  packing.  The  packing-  for  the 
truss  under  consideration  is  shown  in  Fig.  19.  It  is  cus¬ 
tomary  to  draw  first  the  cross-sections  /,  /  of  the  verticals, 
and  show  the  location  of  the  webs  h ,  h  and  side  plates  g,g  of 
the  end  post.  Next,  the  diagonals  z,  z  are  placed  close  to 
the  verticals;  in  the  present  case,  their  inner  surfaces  will  be 
placed  tg  inch  from  the  backs  of  the  channels,  the  same  as  at 
joint  C,  to  allow  f  inch  for  the  height  of  rivet  heads  and 
iV  inch  for  clearance.  The  counter  j  is  connected  to  the 
center  of  the  pin.  Next,  the  eyebars  that  form  the  bottom 
chord  are  placed  in  position  on  the  pins  outside  of  the  diag¬ 
onals,  and  as  close  to  them  and  to  each  other  as  possible. 
In  calculating  the  location  of  the  eyebars  on  the  pins,  it  is 
assumed  that  there  is  -re  inch  space  between  the  heads  of 
eyebars.  The  eyebars  of  the  bottom  chord  are  always 
alternated  on  the  pin;  that  is,  there  is  first  placed  one  that 
comes  from  the  panel  on  one  side,  as  k ,  Fig.  19  (<?),  then  one 
from  the  panel  on  the  other  side,  as  /,  then  k!  and  then  as 
shown,  until  all  the  bars  are  on. 

The  rules  given  in  B.  S.,  Art.  139,  regarding  the  packing 
of  the  bottom  chord  must  always  be  carefully  observed. 
For  example,  it  is  seen  in  Fig.  19  that  no  two  eyebars  in  the 
same  panel  are  in  contact,  and  that  no  eyebar  diverges  from 
the  center  line  by  more  than  iV  inch  per  foot.  The  distances 
from  the  center  of  the  bottom  chord  to  the  various  eyebars 
are  shown  in  Fig.  19;  the  calculation  of  these  distances  is 
simply  a  matter  of  addition. 

27.  In  packing  the  eyebars  on  the  pins,  it  is  seldom 
possible  to  have  any  of  them  exactly  parallel  to  the  center 
line  of  the  chord;  so  that  one  end  of  each  bar  will  usually  be 
farther  from  the  center  line  than  the  other  end,  the  difference 
being  spoken  of  as  the  divergence.  For  example,  the  eye- 
bar  ?zz,  panel  cd,  is  61^  inches  from  the  center  line  at  c, 
and  6Ar  inches  at  d,  so  that  the  divergence  is  6-ft-  —  6  r1^ 
=  i  inch.  In  packing  the  eyebars,  it  is  well  to  determine 
the  allowable  divergence  in  a  panel.  Since,  in  the  present 


32  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


case,  the  panels  are  20  feet  long  and  the  bars  are  allowed  to 
diverge  as  much  as  iV  inch  per  foot  (B.  S .,  Art.  139),  the 
total  allowable  divergence  in  a  panel  is  20  X  iV  =  li  inches; 
that  is,  the  center  of  an  eyebar  cannot  be  more  than  li  inches 
farther  from  the  center  line  at  one  end  than  at  the  other. 

The  dimensions  given  in  Fig.  19  (a)  will  be  discussed  later. 

One  of  the  bottom-chord  pins  will  now  be  designed  to 
illustrate  the  method  of  procedure.  The  same  general 
method  applies  to  the  other  bottom-chord  pins. 

28.  Pins  and  Pin  Plates  at  Joint  d . — In  the  design 
of  the  bottom-chord  pins,  the  conditions  are  somewhat 
different  from  those  in  the  top  chord,  on  account  of  the  fact 
that  in  the  former  the  stresses  in  the  chord  members  are 
entirely  transmitted  from  one  panel  to  the  next  by  means  of 
the  pins.  In  general,  there  are  two  conditions  of  loading  that 
require  to  be  considered.  They  are,  first,  when  the  stresses 
in  the  chord  members  that  meet  at  the  pin  are  maxima, 
and,  second,  when  the  stress  in  the  main  diagonal  that 
connects  to  the  pin  is  a  maximum.  One  of  these  two  condi¬ 
tions  will  always  determine  the  required  diameter  of  the 
pin.  For  each  condition  it  is  necessary  to  calculate  the 
simultaneous  stresses  in  the  members. 

The  pin  at  the  joint  d,  Fig.  9,  will  first  be  designed  for  the 
maximum  chord  stresses  in  cd  and  de ,  which  are  —  272,100 
and  —  340,100  pounds,  respectively,  as  given  in  Fig.  11. 
The  stresses  in  the  chords  are  greatest  when  there  is  a  full 
load  on  the  truss,  under  which  condition  the  counter  dE  is 
out  of  action,  and  the  only  forces  acting  at  d  are  the  stresses 
in  Cd ,  cd ,  de ,  and  D  d,  together  with  the  panel  load  at  d. 
Since  the  floorbeams  are  riveted  to  the  vertical  posts  above 
the  pin,  the  panel  load  at  d  is  applied  to  the  pin  at  the  same 
place  as  the  stress  in  D  d.  The  horizontal  component  in 
Cd ,  when  the  stresses  in  the  chord  members  are  maxima, 
is  equal  to  the  difference  between  the  stresses  \nde  and  cd, 
or  340,100  —  272,100  =  68,000  pounds.  The  vertical  com¬ 
ponent  of  the  stress  in  Cd  is 

68,000  tan  H  —  68,000  X  =  91,800  pounds 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  33 


The  stress  that  is  transmitted  to  the  pin  at  its  contact  with 
the  vertical  must  be  91,800  pounds,  equal  to  the  vertical 
component  in  Cd.  The  forces  that  act  on  pin  d  for  this 
condition  are  shown  in  Fig-.  20. 

As  only  the  components  of  the 
stress  in  Cd  are  required,  it  is 
not  necessary  to  compute  the 
actual  stress  in  this  member. 

For  this  condition,  the  re¬ 
quired  diameter  of  the  pin  is 
found  to  be  4f  inches.  This 
value  will  now  be  verified. 

The  only  member  for  which  the  required  thickness  of  bear¬ 
ing  must  be  computed  is  the  vertical  D  d.  The  greatest 
stress  transmitted  to  the  pin  by  the  vertical  is  greater  than 
that  shown  in  Fig.  20,  since  the  stress  shown  in  Fig.  20  is 

that  in  Dd  when  the  stresses  in  the  chord 
members  are  greatest;  it  is  also  greater 
than  the  stress  in  Dd  shown  in  Fig.  11,  on 
account  of  the  panel  load  applied  to  D  d 
above  d\  it  is  equal  to  the  vertical  component 
of  the  maximum  stress  in  Cd ,  that  is, 

27 


139,000  X 


33.6 


111,700  pounds 


Then,  the  required  thickness  of  bearing  is 

111,700  -  nA  .  . 

— — — — ■  =  1.04  inches 

4.875  X  22,000 

or  .52  inch  on  each  side.  Two  pin  plates 
tV  inch  thick  will  be  riveted  to  the  inside  of 
the  member.  Since  the  web  of  a  9-inch 
15-pound  channel  is  .29  inch  thick,  the  total 
width  of  bearing  on  each  side  of  the  member 
is  .29  -f-  .31  =  .60  inch;  since  the  channels 
are  8i  inches  apart,  the  distance  between 
the  centers  of  bearings  is  7.9  inches.  The  number  of  rivets 

.31 


required  in  each  pin  plate  is 


.60 


X  111,700 


2  X  4,860 


=  6.  The  lower 


34  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


end  of  this  vertical  is  shown  in  Fig.  21.  The  pin  plate  is 
shown  at  a ,  and  the  lower  end  of  the  diaphragm  for  the  floor 
connection  is  shown  at  b. 

The  horizontal  forces  acting  on  the  pin  at  d  are  shown  in 
Fig.  22  (<?),  and  the  vertical  forces  in  Fig.  22  (b) .  The 
bending  moment  due  to  the  vertical  forces  is  constant  from 
g  to  g',  and  equal  to  45,90.0  X  1.175  =  53,930  inch-pounds. 


*0] 

a* 

o 

© 

© 

© 

“5 

00 

© 

d'  i 

1 

c 

d  e 

f  1 

f  < 

, 

J 

J 

/ 

r 

i  J 

i 

4 

*0 

©  © 

9* 

©  © 

© 

© 

©  © 

© 

© 

oo 

**  ** 

oo 

00 

© 

© 

e©  co 

© 

© 

// 

// 

„ 

• 

// 

m '3/, 

L03K 

5375 

,  /S>  Oc"  , 

3375 

—  /  v 

/op] 

IQ3(, 

(a) 


© 

© 

© 


(b) 

Fig.  22 


The  bending  moments,  in  inch-pounds,  caused  at  the  different 
points  by  the  horizontal  forces  are  as  follows: 


at  c,  85,025  X  1.031  . =  87,660 

at  d,  85,025  X  2.062  -  68,025  X  1.031  . =  105,190 


at  <?,  85,025  X  (1.031  +  3.093)  -  68,025  X  2.062  .  .  =  210,380 
at/,85,025  X  (1.969  +  4.031)  -  68,025  X  (.9375  +  3.0)  =  242,300 
It  can  be  seen  that  the  bending  moment  is  greatest  at  /: 
it  is  constant  from  /  to  /'.  Then,  the  greatest  bending 
moment  on  the  pin  is  from  g  to  g',  and  its  value  is 
a'53,9302  +  242, 3002  =  248,230  inch-pounds.  Consulting 
Table  XLI,  since  the  working  stress  in  bending  is  22,000 
pounds  per  square  inch,  it  is  seen  that  a  pin  4j  inches  in 
diameter  has  sufficient  resisting  moment. 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  35 


It  is  necessary,  in  the  calculation  of  bending  moments  due 
to  the  horizontal  forces,  to  calculate  the  moment  at  each 
eyebar  or  other  member;  for,  under  some  conditions  of 
packing,  the  bending  moment  at  some  such  point  as  d  or  e, 
due  to  the  horizontal  forces  alone,  is  greater  than  that  at  any 
other  point  due  to  the  combined  horizontal  and  vertical  forces. 


29.  This  pin  will  now  be  tried  for  the  stresses  on  it 
when  the  stress  in  the  diagonal  Cd  is  a  maximum;  this 
stress  is  given  in  Fig.  11  as  —  139,000  pounds.  The  hori¬ 
zontal  component  of  this  stress  is 

139,000  X  ~~~~  =  82,740  pounds 
33.6 


The  stress  transmitted  to  the  pin  by  the  vertical  under 
this  loading  is  equal  to  the  vertical  component  of  the  stress 
in  Cd,  or,  as  found  in  Art.  28, 

111,700  pounds.  The  simulta¬ 
neous  stresses  in  the  chords  can 
best  be  found  by  considering 
the  live-  and  dead-load  stresses 
separately.  The  maximum  live- 
load  stress  in  Cd  occurs  when 

the  live  load  extends  from  the 

* 

right  end  up  to  joint  d  and  there 
is  no  live  load  to  the  left  of  d\  then,  the  only  external  force 
acting  on  the  truss  to  the  left  of  the  panel  cd  is  the  left 
reaction,  which,  under  these  conditions,  is  evidently  equal  to 
the  shear  in  panel  c  d .  This  was  found  in  Design  of  a  High¬ 
way  Truss  Bridge ,  Part  1,  to  be  70,425  pounds.  Since  there 
are  no  live  external  forces  on  the  truss  to  the  left  of  d,  except 
a  reaction  of  70,425  pounds,  the  live-load  stress  in  cd  is 
70,425  X  40 


226690 


309430 


Fig.  23 


27 


=  —  104,330  pounds 


The  dead-load  stress  is  given  in  Part  1  as  —  122,360 
pounds.  Then,  the  total  stress  in  cd  for  this  loading  is 
104,330  +  122,360  =  226,690  pounds. 

The  stress  in  de  will  be  found  by  adding  to  the  stress 
in  cd  the  horizontal  component  of  the  stress  in  Cd,  which 
•gives  226,690  +  82,740  =  309,430  pounds.  The  forces  acting 


DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §  IS 


O 

*  > 


(i 


on  the  pin  are  shown  in  Fig.  23.  The  horizontal  forces 
acting  on  the  pin  are  shown  in  Fig.  24  (a),  and  the  vertical 
forces  in  Fig.  24  (6).  The  bending  moment  due  to  the 
vertical  forces  is  greatest  from  g  to  g\  and  its  value  is 


(a) 


Cs 

VS 

oc 

vs 

vs 

$ 

vs 

9 

© 

*2 

///s" 

* 

- _  rrn" 

i 

r.y  - - ► 

(b) 


Fig.  24 

55,850  X  1.175  =  65,600  inch-pounds.  The  bending  moments, 
in  inch-pounds,  caused  at  different  points  by  the  horizontal 


forces  are  as  follows: 

at  ct  77,360  X  1.031  . =  79,760 

at  d,  77,360  X  2.062  -  56,670  X  1.031  . =  101,090 


at  e,  77,360  X  (1.031  +  3.093)  —  56,670  X  2.062  .  .  =  202,180 
at  /,  77,360  X  (1.969  -f  4.031)  —  56,670  X  (.9375  +  3)  =  241,000 

The  greatest  bending  moment  is  from  g  to  g' ,  and  is 
V65,6002  +  241, 0002  =  249,800  inch-pounds 

Consulting  Table  XLI,  it  is  seen  that  a  pin  4i  inches  in 
diameter  has  sufficient  resisting  moment;  hence,  it  will  be 
used  for  the  joint  d. 

In  the  present  case,  the  required  diameters,  as  found 
for  the  two  conditions,  are  the  same.  This  is  simply  a 
coincidence;  if  the  diameters  had  come  out  different,  it 
would  have  been  necessary  to  use  the  larger. 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  37 


30.  Pins  at  Joints'  c  and  e. — The  method  of  finding  the 
diameters  of  the  bottom-chord  pins  at  joints  c  and  e  is  entirely 
similar  to  that  given  in  the  preceding  articles,  and  should 
present  no  difficulty.  In  the  present  case,  they  both  work 
out  less  than  that  required  at  d>  but  for  uniformity  they  will 
both  be  made  the  same  size  as  at  d,  that  is,  4i  inches  in 
diameter.  It  is  customary  to  make  all  the  bottom-chord 
pins  the  same  size,  so  that  it  is  necessary  in  each  case  to  find 
the  pin  on  which  the  bending  moment  is  the  greatest.  This 
pin  can  only  be  found  by  trial  and  computation. 

31.  Pin  at  Joint  b. — At  the  joint  b  there  is  no  stress 
transmitted  to  the  chord  from  the  vertical,  but  the  pin  is 
passed  through  plates  in  the  bottom  of  the  vertical,  similar 
to  the  hanger  plates  at  the  top.  The  only  stresses  that  need 
be  considered  at  this  joint  are  the  stresses  in  the  bottom 
chords  ab  and  be.  The  eyebars  on  this  pin  are  not  placed 
close  to  the  vertical,  but  are  so  placed  as  to  run  as  straight 
as  possible  from  joint  c  to  joint  a;  at  the  latter  joint  the  eye- 
bar  is  usually  placed  outside  the  end  post  and  as  close  to  it 
as  practicable. 

32.  Pin  at  Joint  a.—‘ The  forces  acting  on  the  pin  at  the 
joint  a  are  the  stresses  in  a  B  and  a  b ,  the  load  from  the  end 
floorbeam,  and  the  reaction.  The  maximum  stress  in  a  B  is 
+  272,100  pounds.  The  load  from  the  end  floorbeam  is 
given  in  Design  of  a  Highway  Truss  Bridge ,  Part  1,  and  is 
9,644  +  36,250  =  45,894  pounds.  The  reaction  is  equal  to 
the  sum  of  the  vertical  component  in  aB  and  the  load  at  a , 
or  218,615  +  45,894  =  264,510  pounds.  The  stress  in  a  b  is 
given  in  Fig.  11;  but,  as  the  stresses  in  a  B  and  a  b  were  found 
for  different  conditions  of  loading,  there  is  a  slight  incon¬ 
sistency  at  this  joint;  that  is,  the  maximum  stress  in  a  b  is 
not  exactly  equal  to  the  horizontal  component  of  the  maxi¬ 
mum  stress  found  in  a  B.  Under  such  conditions,  it  is  best 
to  take  for  the  stress  in  a  b ,  in  the  design  of  the  pin  at 
joint  a ,  the  horizontal  component  of  the  stress  in  a  B,  or 

272,100  X  =  161,960  pounds, 

33.6 


135—17 


38  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


which  in  this  case  is  a  small  amount  in  excess  of  the  stress 
in  a  b.  The  external  forces  acting  at  the  joint  a  are  shown 

in  Fig.  25.  A  4j-inch  pin  will  be  tried 
first,  this  being  the  size  of  the  remainder 

of  the  bottom-chord  pins. 

% 

The  load  from  the  end  floorbeam  is 
applied  to  the  pin  by  means  of  a  riveted 
chair  or  seat  shown  at  /,  Fig.  7  {b) ,  which 
is  riveted  to  the  end  post,  so  that  this  chair 
-and  the  end  post  act  as  a  single  member 
in  so  far  as  the  load  on  the  pin  is  con¬ 
cerned.  To  find  the  required  combined 
thickness  of  bearing  of  the  chair  and  end 
FlG*  25  post,  it  is  necessary  to  find  the  resultant 

of  the  load  from  the  floorbeam  and  the  stress  in  aB ,  Fig.  25. 
This  is  evidently  the  same  as  the  equilibrant  of  the  reaction 
and  the  stress  in  a  b}  that  is, 

a/264, 510”  +  161,960’  =  310,160  pounds 
The  actual  direction  of  this  resultant  is  of  no  importance; 
it  is  shown  in  its  approximate  position  by  the  dotted  line  in 
Fig.  25.  The  required  thickness  of  bearing  for  the  com¬ 
bined  chair  and  end  post  is,  then, 

310,160 


4.875  X  22,000 


=  2.89  inches, 


or  1.44  inches,  say  lA,  inches  on  each  side.  The  side  plates 
of  the  end  post  are  i  inch  thick;  the  webs  are  A  inch  thick; 
the  side  plates  /  of  the  chair,  Fig.  7  ( b) }  will  be  made  i  inch 
thick;  the  total  thickness  on  each  side  is,  therefore, 
Ire  inches.  It  is  not  necessary  to  calculate  the  number  of 
rivets  required  to  transmit  the  stress  in  the  plate  /  to  the 
floorbeam  and  end  post;  as  a  rule,  if  the  ordinary  rules  of 
rivet  spacing  are  followed,  there  will  be  an  excess.  Since 
the  webs  of  the  end  post  are  Ilf  inches  apart,  the  chair 
plates  will  be  lOf  inches  apart,  and  the  centers  of  bearing 
101  +  1 A  =  12 A  inches  apart.  The  outside  surfaces  of 
the  side  plates  of  the  end  post  are,  then,  12 re  +  lA 
=  13f  inches  apart.  Leaving  i  inch  clearance  on  each  side 
makes  the  inside  surfaces  of  the  eyebars  13i  inches  apart, 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  39 


and  the  centers  of  the  eyebars  14i  inches  apart,  as  shown  in 
Fig.  19  {a). 

The  load  is  transmitted  to  the  abutment  by  means  of  a 
built-up  pedestal,  the  vertical  webs  ?i ,  n ,  Fig.  19  (a) ,  of  which 
are  inside  the  end  post.  The  required  thickness  of  the 
vertical  plates  is 


264,510 
4.875  X  22,000 


2.47  inches, 


or  1.23,  say  li  inches,  on  each  side.  It  is  somewhat  better 
to  make  this  up  with  two  plates  t  inch  thick  than  to  use  one 
li-inch  plate.  The  inside  surfaces  of  the  chair  plates  are 
101  inches  apart.  Leaving  i  inch  clearance  on  each  side 
makes  the  vertical  webs  of  the  pedestal  9|  inches  apart 
center  to  center. 

The  horizontal  forces  acting  on  the  pin  at  a  are  shown  in 
Fig.  26  {a);  the  vertical  forces,  in  Fig.  26  {b) .  The  bend¬ 
ing  moment  due  to  the  horizontal  forces  is  80,980  X  1.344 
=  108,840  inch-pounds,  and  is  constant  from  c  to  c';  that 


*1344 


—  Z2./875 

(a) 


© 

oo 

Ci 

© 


1 1 


© 

00 

C5 

o 

00 


/.344 


Fig.  26 

due  to  the  vertical  forces  is  132,265  X  1.469  =  194,300  inch- 
pounds,  and  is  constant  from  d  to  d' .  The  greatest  bending 
moment  on  the  pin  is  then  from  d  to  d',  and  is 

Vl08340“  +  194,300"  =  222,700  inch-pounds 


40  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


Consulting  Table  XLI,  it  is  seen  that  a  pin  4f  inches  in 
diameter  has  a  sufficient  resisting  moment;  but,  as  x  the 
remaining  bottom-chord  pins  are  to  be  made  4%  inches  in 
diameter,  the  latter  size  will  be  used  for  joint  a  also.  The 
detail  of  joint  a  will  be  discussed  presently. 


BEARINGS 

33,  Required  Area. — The  required  area  of  bearing 
for  each  end  of  each  truss  is  found  by  dividing  the  reaction 
by  the  working  pressure  on  the  masonry.  Since  the 
reaction  is  264,510  pounds,  and  the  masonry  is  cement 
concrete,  on  which  the  working  pressure  is  400  pounds  per 
square  inch  ( B .  S.,  Art.  103),  the  required  area  of  bearing 
is  264,510  -7-  400  =  661.3  square  inches.  If  the  bedplate  is 
made  square,  it  should  be  about  26  inches  square.  The 
actual  dimensions  depend  on  other  details,  such  as  rollers,  etc. 

34.  Pedestal. — Built-up  pedestals  like  that  shown  in 
Fig.  27  are  used  for  pin-connected  trusses.  The  bottom  of 
the  pedestal  is  made  the  same  length  as  the  length  of  the 
bedplate;  the  width  depends  somewhat  on  the  distance 
between  the  vertical  webs,  which  are  just  inside  the  end  post. 
The  height  of  the  pedestal  depends  on  the  allowable  distance 
from  the  bottom  of  the  truss  to  the  top  of  the  bridge  seat; 
it  is  desirable  to  keep  the  top  of  the  bridge  seat  above  high 
water.  In  general,  the  height  should  be  about  one-half  the 
length;  hence,  in  this  case  it  will  be  made  15  inches. 

In  Fig.  27,  (a)  is  the  elevation  of  joint  a,  and  shows  the 
pedestal,  the  rollers,  and  the  chair  e  that  supports  the  end 
floorbeam;  ( b )  is  an  end  view  of  the  joint;  (c)  is  a  top  view 
of  the  pedestal;  and  (d)  is  a  top  view  of  the  rollers.  The 
bottom  plate  /  of  the  pedestal  is  generally  made  about 
li  inches  thick,  and  the  angles  g,g  that  connect  the  vertical 
webs  h  to  the  base  plate  /  are  made  6  in.  X  6  in.  X  f  in. 
The  rivets  that  connect  the  angles  g  to  the  plate  /  are  counter¬ 
sunk  on  the  under  side.  The  diaphragms  i,  i  are  riveted  to 
the  vertical  webs  to  stiffen  the  pedestal.  In  the  chair  e ,  a 
diaphragm  j  is  inserted  between  the  side  plates,  in  order  to 


(C) 


p 


m  n 


2 

n 


r*» 

±± 


(d) 


-o 


P 


Til 


i 

#1 


a 


JSir 


2= 


Q 

Q 


Q 

Q 

Q 

i 


r 


*  i 

I  U--V 

•  I  > 

-»-Fl  , 

I  pr«g 


hJ 


S' 


mil// 


S 


A; 


# 


-# 


41 


Fig.  27 


42  DESIGN,  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


distribute  the  load  from  the  floorbeam  more  evenly  between 
the  two  sides.  At  one  end  of  the  bridge,  the  fixed  end,  the 
base  plate  /  rests  directly  on  the  masonry,  and  is  anchored 
to  it  by  means  of  anchor  bolts.  At  the  other  end,  rollers  are 
placed, under  the  plate  /,  as  shown  at  k ,  in  order  to  allow 
that  end  to  move  back  and  forth  as  the  temperature  changes. 

35.  Rollers. — The  allowable  pressure  per  linear  inch 
on  the  rollers  is  given  in  B.  A.,  Art.  103,  as  600  D.  In 
the  present  case,  the  smallest-sized  roller  (3  inches,  B.  S., 
Art.  153)  gives  sufficient  resistance  to  transmit  the  reac¬ 
tion,  as  will  be  shown  presently.  It  is  customary  to  space 
the  rollers  about  i  inch  apart  for  the  full  length  of  the 
pedestal.  In  the  present  case,  if  the  end  rollers  /,  /  are  each 
placed  i  inch  from  the  end  of  the  plate  /,  there  is  just  room 
for  nine  rollers  in  the  length  of  the  pedestal.  The  rollers 
are  usually  made  at  least  as  long  as  the  distance  between 
the  outside  edges  of  the  base  angles  in  this  case  about 
23  inches.  Nine  rollers  at  23  inches  gives  207  linear  inches 
of  rollers,  which,  at  600  X  3  =  1,800  pounds  per  linear  inch, 
can  support  372,600  pounds.  As  this  is  greater  than  the 
reaction,  these  rollers  (that  is,  nine  rollers  23  inches  long) 
are  sufficient.  If  the  allowable  load  had  been  less  than  the 
reaction,  it  would  have  been  necessary  to  use  either  longer 
rollers  or  rollers  of  larger  diameter. 

The  rollers  are  fastened  together  so  as  to  form  what  is 
known  as  a  roller  nest,  in  the  manner  shown  in  Fig.  27  (d). 
Short  bolts  rn,m ,  known  as  studs,  about  f  inch  in  diameter, 
are  set  into  the  ends  of  each  roller  about  li  inches,  and  the 
ends  left  to  project  2  inch  at  each  end.  A  flat  ,bar  71  is 
placed  on  each  end  of  the  rollers,  and  the  short  bolts  fit  into 
holes  in  this  bar.  The  bars  n  are  kept  in  position  by  the 
bolts  0  and  additional  bars  p  at  each  end  of  the  nest;  the 
bars  p  are  i  inch  longer  than  the  rollers,  and  are  inserted 
between  the  ends  of  the  side  bars  n .  A  plate  about  2  inches 
in  thickness  is  inserted  under  the  rollers  to  give  them  a 
smooth -surface  to  roll  on,  and  also  to  distribute  the  pressure 
more  evenly  over  the  masonry.  The  bearing  surfaces  above 


78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  43 


and  below  the  rollers  are  provided  with  projections  q  that  fit 
into  grooves  r  planed  in  the  rollers,  and  are  for  the  purpose 
of  preventing  the  pedestal  and  rollers  from  moving  sidewise. 
The  base  plate* of  the  pedestal  and  the  bedplate  are  con¬ 
tinued  out  beyond  the  ends  of  the  rollers  a  sufficient  distance 
(generally  3i  or  4  inches)  to  allow  the  insertion  of  the 
anchor  bolts  s  that  hold  the  pedestal  and  bedplate  in  posi¬ 
tion.  At  the  expansion  end,  the  holes  in  the  base  plate 
through  which  the  anchor  bolts  pass  are  made  just  wide 
enough  to  allow  the  insertion  of  the  bolts,  and  long  enough, 
as  sho\yn  at  t ,  to  allow  the  base  plate  and  pedestal  to 
move  backwards  and  forwards. 


LATERAL  CONNECTIONS 

36.  Upper  ^Lateral  Truss. — Fig.  28  shows  the  connec¬ 
tion  of  the  diagonals  of  the  upper  lateral  truss  to  the  top  of 
the  top  chord:  a  and  b  are  the  diagonals,  and  c  and  d  are 


Fig.  28 


lug  angles  that  help  to  connect  a  and  b  to  the  connection 
plate  <?.  This  plate  also  acts  as  a  tie-plate  for  the  top  chord, 
being  extended  out  a  sufficient  distance  to  allow  the  connec¬ 
tion  of  the  laterals.  The  top  flange  of  the  transverse  frame 
is  also  riveted  to  this  connection  plate;  the  holes  for  the 
connection  are  shown  at  /. 

37.  Transverse  Frame. — Fig.  29  shows  the  connection 
of  the  transverse  frame  to  the  truss.  The  upper  flange  a  is 


44  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  §78 


riveted  to  the  connection  plate  e  on  top  of  the  top  chord,  as 
explained  in  the  preceding  article.  These  angles,  together 
with  the  web  members  b  and  the  bottom  flange  angles,  are 
connected  to  the  connection  plate  c,  which  is  riveted  to 
the  vertical  post  of  the  truss  by  means  of  the  connection 


angles  d;  the  plate  c  is  usually  made  -ft-  inch  thick,  and  the 
angles  d  not  less  than  3  in.  X  3  in.  X  tg  in.  The  web  mem¬ 
bers  b  of  the  frame  are  connected  to  the  top  and  bottom 
flanges  by  means  of  the  iVinch  plates  /.  The  bracket  below 
the  frame  is  composed  of  the  iVinch  web  g\  the  angle  ht 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  45 


the  same  size  as  the  bottom  flange  angles;  the  curved 
angles  i,  generally  2i  in.  X  2i  in.  X  in.;  and  the  connec¬ 
tion  angles — continuations  of  the  angles  d  shown  above. 

38.  Portal. — The  connection  of  the  portal  to  the  end 
post  corresponds  to  the  connection  of  the  transverse  frame 
that  was  just  described.  On  account  of  the  portal  being 
inclined,  however,  the  top  flange  angles  are  connected  to  the 
top  chord  in  the  manner  shown  in  Fig.  17  at  p  and  o.  The 
bent  plate  o  is  continued  out  beyond  the  edge  of  the  top 
chord,  and  serves  as  the  connection  plate  for  the  diagonal  in 
the  end  panel  of  the  upper  lateral  truss,  in  the  same  way  that 
the  plate  e  serves  this  purpose  in  Figs.  28  and  29. 


BRIDGE-SEAT  PLAN 

39.  Fig.  30  is  the  bridge-seat  plan  for  the  bridge  that 
has  just  been  designed.  The  distance  between  the  centers 
of  bedplates  or  pedestals  d,  d  is  shown  equal  to  the  span,  in 
this  case  160  feet.  The  fronts  of  the  pedestals  are  placed 
1  foot  from  the  neat  line  of  the  abutment,  making  the  neat 
lines  2  feet  3  inches  from  the  center  of  the  pedestal  at  each 
end,  or  155  feet  6  inches  apart.  The  face  of  the  parapet  is 
placed  6  inches  from  the  back  edge  of  the  pedestal  and 
1  foot  9  inches  from  the  center  of  the  pedestal.  This  makes 
the  bridge  seat  4  feet  wide  from  neat  line  to  parapet.  It  is 
common  practice  to  make  the  bridge-seat  stone*  2  feet  thick 
for  a  span  of  this  length,  and  to  have  it  project  about  6  inches 
bevond  the  neat  line. 

The  distance  from  the  top  of  the  floor  to  the  top  of  the 
bridge  seat  is  found  by  adding  together  the  vertical  distances 
occupied  by  stringers,  floorbeams,  rollers,  pedestals,  etc. 
In  Fig.  1  it  can  be  seen  that  the  distance  from  the  top  of 
the  floor  to  the  center  of  the  pins  in  the  bottom  chords  is 
5  feet  3i  inches.  In  Art.  34,  it  was  decided  to  make  the 
pedestal  1  foot  3  inches  from  the  center  of  the  pin  to  the 
bottom.  Then,  the  distance  from  the  top  of  the  floor  to 
the  top  of  the  bridge  seat  at  the  fixed  end  (right-hand 
end)  is  6  feet  6i  inches.  At  the  roller  end,  the  distance  is 


46 


155~6  "c/ear  6efwees?  neat  L/hes 


§78  DESIGN  OF  A  HIGHWAY  TRUSS  BRIDGE  47 


increased  by  the  rollers  3  inches  in  diameter  and  the  bed¬ 
plate  2  inches  in  thickness,  making  the  distance  6  feet 
Hi  inches,  as  shown  in  Fig.  30. 

The  top  of  the  parapet  is  sometimes  finished  even  with 
the  top  surface  of  the  sidewalk  and  roadway.  This  is 
objectionable  because  the  parapet  makes  a  rigid  surface 
over  which  the  traffic  must  pass.  This  surface  does  not 
wear  down  as  fast  as  the  approach  leading  to  the  bridge, 
with  the  result  that  it  forms  a  lump  or  ridge  at  each  end, 
and  this  is  a  great  inconvenience  to  the  traffic.  A  somewhat 
better  method  is  to  finish  the  parapets  level  with  the  tops  of 
the  stringers,  so  that  the  floor  plank  can  be  continued  over 
them.  In  Fig.  30,  the  parapet  from  a  to  b  is  level  with  the 
tops  of  the  sidewalk  stringers,  that  from  b  to  c  is  level  with 
the  tops  of  the  roadway  stringers,  and  that  from  c  to  c  is  level 
with  the  tops  of  the  stringers  under  the  railway  track. 


<• 


DESIGN  OF  A  RAILROAD 
TRUSS  BRIDGE 


Note. — The  tables  referred  to  in  this  Section  are  the  Bridge  Tables 
furnished  with  the  Course.  The  abbreviation  B.  S.  stands  for  Bridge 
Specifications ,  which  forms  another  Section  of  the  Course. 

In  order  to  shorten  the  work,  the  correct  shape  will  invariably  be 
chosen  the  first  time  in  the  following  pages.  The  method  of  arriving 
at  the  correct  shape  by  trial  has  been  illustrated  sufficiently  in  preceding 
Sections. 


DATA 

1.  General  Data. — In  this  Section,  a  through  railroad 
truss  bridge  will  be  designed  according  to  the  data  given 
on  the  next  page.  In  order  to  illustrate  the  method  of 
designing  such  a  bridge,  each  member  will  be  designed  in 
detail.  Many  of  the  steps  taken  in  the  following  pages  are 
performed  mentally  by  experienced  designers;  it  is  necessary 
for  beginners,  however,  to  perform  almost  all  the  operations 
as  given  here. 

2.  Kind  of  Bridge. — As  the  maximum  allowable  dis¬ 
tance  from  the  base  of  rail  to  the  underneath  clearance  line 
is  4  feet,  it  is  evident  that  a  through  bridge  must  be  used. 
As  the  span  is  less  than  150  feet,  riveted  trusses  will  be  used 
{B.  S.,  Art.  14) .  Trusses  for  railroad  bridges  are  usually 
made  slightly  deeper  than  those  for  highway  bridges,  the 
depth  being  generally  from  one-fifth  to  one-sixth  of  the 
length.  In  the  present  case,  an  approximate  mean  will  be 
chosen  between  these  ratios,  and  the  trusses  will  be  made 
26  feet  6  inches  deep.  In  B.  S.,  Art.  229,  it  is  stated  that, 
for  riveted  truss  bridges,  panel  lengths  of  from  15  to  20  feet 
are  best;  in  the  present  case,  eight  panels,  18  feet  each,  will 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

‘i  79 


2 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


For  bridge  over, 
at _ 


General  Data 

Highway  and  river 


Oberlin,  Ohio 


Length  and  general  dimensions  ®ne  sPan  144  center  to  center  of 
bearings ,  to  span  the  river  and  the  highway  on  one  side  of  the  river 


Angle  of  abutments  with  center  line  of  bridge. 


90c 


Width  of  bridge  and  location  of  trusses .  Clear_distance  between  trusses 
14  feet  . 

Floor  system  Standard  ties  on  steel  stringers  ( B .  S.,  Art.  48) 

Number  and  location  of  tracks  O™  steam^ailroad^  track  a/  cento r_  ot 
bridge  * 


Loading. 


Cooper' s  E50 


Granite  abutments 


Description  of  abutments- _ _ _ _ 

Distance  from  floor  to  clearance  line _ Not  over  4  feet  below  base  of  rail 


“  “  to  high  water. 
“  “  to  low  water. 


11  feet 


22  feet 


<  < 


“  “  to  river  bottom. 

Character  of  river  bottom _ , _ 


23  feet 


Solid  rock 


Usual  season  for  floods _ 

Name  of  nearest  railroad  station. 
Distance  to  nearest  “  “ 

Time  limit _ : _ , _ _ _ 


April  and  May 


Oberlin ,  Ohio 


2  miles 


Six  months 


Name  of  Engineer.. 
Address  of  “ 


International  Correspondence  Schools 
Scranton,  Pa. 


Remarks  'N°P  highway  at  side  ot  river  is  16  feet  below  base  of  rail , 
and  12  feet  headroom  is  required ,  leaving  4  feet  as  the  maximum  depth 
of  floor  from  the  base  of  rail 


§  7!)  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


o 

o 


be  used,  as  shown  in  Fig.  1.  This  will  make  the  angle 
between  the  diagonals  and  the  horizontal  about  56°,  which 
is  a  good  angle  ( B .  S .,  Art.  15). 


3.  Width,  of  Bridge. — In  the  data,  it  is  stated  that  there 
will  be  one  steam-railroad  track  at  the  center  of  the  bridge. 
The  required  distance  from  the  center  line  of  the  track  to 
the  inside  of  the  truss  is  given  in  B.  S.,  Art.  18,  as  7  feet, 
which  makes  the  required  clear  width  14  feet.  Assuming 
that  each  truss  will  occupy  a  width  of  2  feet,  the  distance 
center  to  center  of  trusses  is  16  feet.  In  case  the  width  of 
the  truss  comes  out  1  or  2  inches  more  or  less  than  the 
assumed  width,  it  is  unnecessary  to  revise  the  design;  the 
correction  can  be  effected  by  making  the  floorbeams  of  such 
length  that  there  will  be  14  feet  clear  width. 


DESIGN  OF  FLOOR  SYSTEM 


STRINGERS 

4.  Spacing  and  Depth,  of  Stringers.— The  stringers 
will  be  spaced  6  feet  6  inches  center  to  center  {B.  S .,  Art.  16) . 
In  B.  S.,  Art.  49,  it  is  specified  that  the  depth  of  the  stringers 
shall  be  not  less  than  one-eighth  of  the  panel  length;  in  this 
case,  therefore,  the  least  allowable  depth  is  =  2.25  feet. 
It  is  advisable,  when  possible,  to  use  a  somewhat  greater 
depth  in  order  to  get  greater  stiffness;  the  stringers  will  be 
made  2.5  feet,  or  30  inches,  deep.  As  this  depth  is 
greater  than  that  of  the  deepest  I  beam,  a  plate  girder 
must  be  used. 

5.  Eive-Eoad  Shears  and  Moments. — -The  live  load 
that  goes  to  one  line  of  stringers  and  to  one  truss  is  equal 


4 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


09Z9TQ 

09Z9TQ, 


02Z9TQ 

09Z9TQ 


TT 

•o 


*4 


o> 


to  one-half  of  Cooper’s  E50  loading,  as 
shown  in  Fig.  2.  The  maximum  bending 
moment  caused  on  a  stringer  by  this  load¬ 
ing  is  found  as  explained  in  Stresses  in 
Bridge  Trusses ,  Part  4:  it  occurs  at  the 
center  of  the  panel  when  the  loads  are  in 
the  position  shown  in  Fig.  3,  and  is  equal 
to  212,500  foot-pounds.  The  maximum  end 


Fig.  3 


0009Z 

0009Z 

0002Z 

9009Z 


G 

G 

G 

G 


ooszrQ 


09Z9TQ 


09Z9TQ 

09Z9TQ 


09Z9TQ 


OOOffZ 

ooosz 

9009Z 

0009Z 


G 

G 

G 

G 


oosziQ 


24 


24  " 


o' 

M 


‘O 


G 


*4 


VO 

A 


g 


*4 


.  "D 

u 


shear  occurs  when  the  loads  are  in  the 
position  shown  in  Fig.  4,  and  is  equal  to 
58,330  pounds.  The  maximum  live-load 
shear  at  a  section  5  feet  from  the  end, 
which  must  be  computed  for  the  determi¬ 
nation  of  the  rivet  pitch  (see  Design  of  Plate 
Girders ,  Part  1),  is  found  to  be  33,330 
pounds.  As  will  be  seen  presently,  it  is 


25000 

© 

C> 

© 

JO 

** 

25000 

r 

s' 

o' 

* 

m  D  *■ 

nt 

*  O  - H 

J  * 

Fig.  4 


unnecessary  to  compute  the  maximum  shear 
at  any  other  section. 

6.  Impact  and  Vibration. — Since  the 
stringer  is  a  floor  member,  the  amounts  to 
be  added  to  the  shears  and  moments,  to 
allow  for  impact  and  vibration,  are  as  fol¬ 
lows  ( B .  S.,  Art.  25):  to  the  moment, 
212,500  foot-pounds;  to  the  shear  at  the 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


5 


end,  58,330  pounds;  to  the  shear  at  5  feet  from  the  end. 
33,330  pounds. 

7.  Wind  Pressure. — The  wind  pressure  on  the  train 
increases  the  amount  of  load  that  goes  to  the  leeward  stringer. 
The  center  of  wind  pressure  is  7  feet  above  the  top  of  the 
rail  ( B .  S.,  Art.  27)  and  about  8  feet  above  the  top  of  the 
stringers.  The  center  of  moments  will  be  taken  at  the  top 
of  the  stringers.  Then,  since  the  wind  pressure  is  300  pounds 
per  linear  foot  ( B .  S .,  Art.  27),  and  the  stringers  are  6  feet 
6  inches  center  to  center  ( B .  S.,  Art.  48),  the  increase  in 


load  on  the  leeward  stringer  is 


300  X  8 
6.5 


=  369.23  pounds  per 


linear  foot.  The  bending  moment  ’due  to  this  increase,  at 
the  section  where  the  live-load  bending  moment  is  greatest, 
that  is,  at  the  center  of  the  panel,  is  14,950  foot-pounds;  the 
shear  at  the  end  is  3,323  pounds,  and  at  a  section  5  feet  from 
the  end,  1,477  pounds. 


8.  Dead-Load  Moments  and  Shears. — The  weight 
of  the  track  will  be  assumed  as  400  pounds  per  linear  foot, 
one-half  of  which,  or  200  pounds  per  linear  foot,  is  carried 
by  each  stringer.  The  weight  of  the  stringer  will  be  assumed 
to  be  150  pounds  per  linear  foot,  which  makes  the  total  dead 
load  350  pounds  per  linear  foot.  The  bending  moment  due 
to  this  dead  load,  at  the  section  where  the  live-load  moment 
is  greatest,  that  is,  at  the  center  of  the  panel,  is  14,180  foot¬ 
pounds;  the  shear  at  the  end  is  3,150  pounds,  and  at  a  section 
5  feet  from  the  end,  1,400  pounds. 

9.  Total  Moments  and  Shears. — The  total  shears  and 
moments  are  as  follows: 

Total  maximum  moment,  212,500  4-  212,500  +  14,950 
-f  14,180  =  454,130  foot-pounds. 

Total  shear  at  the  end,  58,330  +  58,330  +  3,320  -f  3,150 
=  123,130  pounds. 

Total  shear  5  feet  from  the  end,  33,330  -f-  33,330  +1,480 
+  1,400  =  69,540  pounds. 

10.  Design  of  Web. — It  was  decided  in  Art.  4  to  have 
the  web  30  inches  deep.  The  thickness  will  be  made  inch. 

135—18 


6 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


Then,  the  intensity  of  shearing  stress  at  the  end  is 

— - v-  =  7,297  pounds  per  square  inch.  Consult- 

30  X  Te  (16.8/5) 

ing  Table  XXXVI,  it  is  seen  that  the  least  unsupported 
distance  for  the  web  is  25  inches,  and,  as  the  vertical 
legs  of  the  flange  angles  will  probably  be  closer  together 
than  this,  no  stiffeners  will  be  required.  It  is  therefore 
unnecessary  to  find  the  intensity  of  shearing  stress  at  any 
other  section. 


11.  Design  of  Flanges. — The  required  area  of  flange 
will  be  found  by  the  following  formula,  given  in  Design  of 
Plate  Girders ,  Part  1: 


A  = 


M 
s  h9 


th 

T 


In  the  present  case,  everything  is  known  except  hs.  It  has 
been  seen  in  the  preceding  Sections  that  hg  is  usually  less 
than  the  width  of  web;  in  this  case,  it  will  be  assumed  to  be 
27  inches.  Then, 


A  = 


454,100  X  12  30  X 


1  6 


12.61  -  2.11 


16,000  X  27  8 

=  10.50  square  inches 

Two  angles  6  in.  X  6  in.  X  i  in.  will  be  used  for  both  the 
top  and  the  bottom  flanges.  The  gross  area  of  the  two  angles 
(Table  IX)  is  11.5  square  inches,  and  the  net  area,  deducting 
one  -g-inch  rivet  hole  from  each  angle,  is  10.5  square  inches. 
The  distance  between  the  centers  of  gravity  of  the  flanges  is, 
then,  30.25  —  1.68  —  1.68  =  26.89  inches,  and,  therefore, 

454,100  X  12 


A  = 


2.11  =  12.67  -  2.11 


16,000  X  26.89 

=  10.56  square  inches. 

Two  angles  6  in.  X  6  in.  X  i  in.  are,  therefore,  sufficient 
for  the  top  flange  and  near  enough  the  required  size  for  the 
bottom  flange. 


12.  Lateral  Bracing  Between  Stringers. — Since  the 
web  is  inch  thick  and  the  top  flange  angles  are  6  inches 
wide,  the  width  of  the  top  flange  is  12i96  inches.  Since  the 
panel  length  is  18  feet,  it  is  greater  than  12  times  the  width 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


7 


of  the  flange,  and,  according  to  B.  S.y  Art.  87,  lateral  bracing 
is  required  between  the  top  flanges.  This  will  be  made  of 
the  same  general  form  as  used  in  the  Section  on  Deng?i  of 
Plate  Girders ,  Part  2. 


13.  Flange  Iiivets. — The  flange  rivets  are  f  inch  in 
diameter,  shop  driven,  in  double  shear,  and  in  bearing  on 
the  iVinch  web;  the  latter  value,  10,830  pounds,  is  the 
smaller.  Since  the  center  line  between  the  two  rivet  lines 
of  a  6-inch  leg  is  3f  inches  from  the  back  of  the  angle,  and 
the  flanges  are  30f  inches  back  to  back,  the  distance  hr 
between  the  centers  of  the  rivet  lines  is  30f  —  3f  —  3f 
=  23i  inches.  Then,  the  required  pitch  of  the  rivets  at 

K  h 

the  end  of  the  stringer,  as  found  from  the  formula  p  —  - 
( Design  of  Plate  Girders ,  Part  1),  is 


10,830  X  23.5 
123,130 


=  2.07  inches; 


and  at  5  feet  from  the  end, 

10,830  X  23.5 
69,540 


3.66  inches 


As  the  ties  will  rest  directly  on  top  of  the  top  flange,  the 
required  pitch  of  rivets  in  the  top  flange  is  nine-tenths  of 
the  above,  that  is,  1.86  inches  at  the  end  and  3.29  inches  at 
5  feet  from  the  end. 

For  practical  reasons,  the  rivet  spacing  in  the  top  flanges 
of  the  stringers  in  railroad  bridges  should  not  exceed 
3i  inches,  the  principal  reason  being  the  fact  that  these 
rivets  transmit  the  load  directly  to  the  web.  The  pitch  is 
usually  taken  to  the  next  lower  i  inch.  Then,  the  rivets  in 
the  top  flange  will  be  spaced  If  inches  apart  at  the  end  and 
3i  inches  apart  at  5  feet  from  the  end.  Between  these  sec¬ 
tions,  the  pitch  is  gradually  changed  at  the  rate  of  about 
2  inch  each  time,  making  the  successive  pitches  If,  2f,  2f, 
and  3f  inches.  It  is  customary  to  make  each  of  these  cover 
approximately  the  same  distance  as  far  as  conditions  will 
permit.  For  example,  in  the  present  case,  the  following 
spacing  may  be  used: 


Base  of  Rail 


o 


s> 


G 


<s 
_ 1_ 


*P2 

/t 


C  1)000 


•  ••••• 


G'sG  G  vi 


f*7 

o 


7* 


^?g 


KJ>  VA. 

•  ®  •'? 
•  •  • 

M'  ^  Vj^ 

•  •  • 

Vi 

•  •  • 

G  G  G  G  , 

,G^G  G  G 

G 

G 

$ 

G 


o 

>-• 

fe 


^  £ 


d  (a)  2;  "=/B 


§  71)  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  9 

12  spaces  at  If  inches  =  1  foot  9  inches 

10  spaces  at  2f  inches  =  1  foot  10i  inches 

6  spaces  at  2f  inches  =  1  foot  4i  inches 

Total  distance  =  5  feet 

Beyond  the  section  at  5  feet  from  the  end,  a  few  spaces  at 
3f  inches  can  be  inserted,  and  then  a  pitch  of  3i  inches  used 
throughout  the  remainder  of  the  flange  as  far  as  the  3i-inch 
pitch  at  the  other  end. 

14.  Connection  of  Stringer  to  Floorbeam. — In  the 
design  of  the  highway  bridge  in  the  preceding  Sections,  the 
design  of  the  floor  connections  was  left  until  after  the  design 
of  the  trusses.  In  the  present  case,  the  connections  of  the 
stringer  to  the  floorbeam  will  be  designed  now,  for  in  rail¬ 
road  bridges  it  is  much  less  difficult  to  decide  on  the  type 
of  connection.  Fig.  5  shows  a  typical  connection:  A  A, 
Fig.  5  ( a ),  is  the  usual  cross-section  of  the  floorbeam,  and 
B  B,  Fig.  5  (b) ,  is  the  cross-section  of  the  stringer.  The 
latter  rests  on  a  shelf  angle  c  that  is  riveted  to  the  bottom 
flange  angles  of  the  floorbeam;  the  connection  angles  d  are 
placed  outside  of  the  flange  angles  of  the  stringer,  and  tight 
fillers  e  are  placed  between  them  and  the  web.  Tight  fillers 
or  reinforcing  plates  /  are  also  riveted  to  the  web  of  the 
floorbeam.  With  this  style  of  connection,  the  smallest  value 
of  the  rivets  that  connect  the  angles  to  the  stringer  is 
13,200  pounds  (f-inch  rivets,  shop  driven,  in  double  shear), 
and  that  of  the  rivets  that  connect  the  angles  to  the  floorbeam 
is  5,410  pounds  (|--inch  rivets,  field  driven,  in  single  shear). 
Then,  the  number  of  rivets  required  to  connect  the  angles 
to  the  stringer  and  to  the  floorbeam  is,  respectively,  since 

the  end  shear  is  123,130  pounds,  =  9.3  rivets,  and 

193  130 

— ? - =  22.8  rivets.  It  is  customary  to  use  the  next 

5,410 

larger  even  number,  24  in  this  case,  for  the  latter,  and  half 
this  number,  12  in  this  case,  for  the  former,  as  shown  in 
Fig.  5.  As  it  is  impossible  to  get  this  number  of  rivets  in  a 
single  row  without  getting  the  rivets  too  close  together, 


10  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


6-inch  angles  are  used,  giving  room  for  two  rows  in  each 
leg.  The  least  allowable  thickness  of  connection  angle  is 
h  inch  ( B .  S .,  Art.  51),  so  6"  X  6"  X  A"  angles  are  used. 
It  is  well  to  make  the  thickness  of  the  connection  angles  at 
least  equal  to  that  of  the  stringer  web.  Had  the  stringer 
web  been  f  inch  thick,  6"  X  6"  X  i"  connection  angles  would 
have  been  used. 


INTERMEDIATE  FLOORBEAMS 

15.  Length  and  Depth. — The  length  of  the  floorbeam 
will  be  taken  as  16  feet,  the  distance  center  to  center  of  the 
trusses.  When  the  connection  represented  in  Fig.  5  is  used, 


Fig.  6 

the  floorbeam  is  made  1  foot  deeper  than  the  stringer;  if 
this  does  not  give  a  depth  equal  to  one-sixth  the  length 
( B .  S.,  Art.  49),  the  shelf  angles  are  placed  farther  from 
the  bottom  flange,  and  stiffeners  are  placed  under  them. 
The  top  flange  of  the  floorbeam  should  never  be  more  than 

about  6  inches  above 
the  top  of  the  string¬ 
ers,  as  it  will  inter¬ 
fere  with  the  rail  if  it 
*>  . 

§  is  higher  than  this. 
In  the  present  case, 
a  web  42  inches  in 

width  will  be  used  for  the  floorbeam. 

16.  Live-Load  Shears  and  Moments. — The  live  load 
that  comes  on  the  floorbeam  from  one  line  of  stringers  is 
greatest  when  the  loads  are  in  the  position  shown  in  Fig.  6, 
and  is  equal  to  75,830  pounds.  As  the  stringers  are  6  feet 
6  inches  apart,  and  the  floorbeam  is  16  feet  long,  the  loads 


Fig.  7 


§  79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


11 


are  applied  to  the  floorbeam  as  shown  in  Fig.  7,  the  shear 
from  the  truss  to  the  stringer  being  75,830  pounds,  and  the 
bending  moment  on  the  floorbeam  at  the  stringer  connection 
being  75,830  X  4.75  =  360,200  foot-pounds.  This  is  also  the 
value  of  the  bending  moment  at  the  center,  as  it  is  constant 
between  the  stringer  connections. 

17.  Impact  and  Viblation. — Since  the  floorbeam  is  a 
floor  member,  the  amounts  that  must  be  added  to  the  shear 
and  moment  to  provide  for  the  effect  of  impact  and  vibration 
are  as  follows:  to  the  shear,  75,830  pounds;  and  to  the 
moment,  360,200  foot-pounds  ( B .  S.,  Art.  25). 


Or 

§ 

© 

© 


© 

© 


4.751 


© 

§ 

© 


6.5 
-  /6‘ 


© 

© 

N 

0* 


4.?5- 


18.  Wind  Pressure. — In  Art.  7  it  was  found  that  the 
wind  pressure  on  the  train  increased  the  load  on  the  leeward 
stringer  by  369.23  pounds  per  linear  foot.  Then,  the  increase 
in  the  load  on  the  floorbeam  at  the  leeward  stringer  connec¬ 
tion  is  18  X  369.23  =  6,650  pounds.  There  will  be  a  cor¬ 
responding  decrease 
in  the  load  on  the 
windward  stringer, 
as  shown  in  Fig.  8, 
in  which  the  increase 
and  the  decrease  are 
shown  as  a  downward 
and  an  upward  force,  respectively,  instead  of  adding  them 
to  ai*d  subtracting  them  from  the  loads  shown  in  Fig.  7. 
Taking  moments  about  the  right  end  of  the  floorbeam,  the 
reaction  at  the  left  end,  which  is  also  the  shear  from  the 
truss  to  the  stringer,  is  found  to  be  2,700  pounds,  and 
the  bending  moment  at  the  left-hand  stringer,  2,700  X  4.75 
=  12,800  foot-pounds.  It  is  unnecessary  to  find  the  shear 
and  moment  at  the  other  end,  as  they  simply  tend  to  decrease 
those  due  to  live  load. 


Fig.  8 


19.  Dead  Doad. — The  dead  load  on  each  stringer 
(Art.  8)  is  350  pounds  per  linear  foot;  the  amount  that  goes 
to  the  floorbeam  at  each  stringer  connection  is  then  350  X  18 
=  6,300  pounds.  The  weight  of  the  floorbeam  will  be 
assumed  to  be  200  pounds  per  linear  foot.  The  dead-load 


12  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


shear  at  the  end  is  then  7,900  pounds,  and  the  bending 
moment  at  the  stringer  connection  is  36,300  foot-pounds. 

20.  Total  Shear  and  Moment. — The  total  shear  and 
moment  are  as  follows: 

Total  shear  at  the  end,  75,830  +  75,830  +  2,700  +  7,900 
=  162,260  pounds. 

Total  bending  moment  at  the  stringer,  360,200  -f  360,200 
+  12,800  -j-  36,300  =  769,500  foot-pounds. 

» 

21.  Design  of  Web. — In  Art.  15  it  was  decided  to 
make  the  web  of  the  floorbeam  42  inches  deep.  A  thickness 
of  f  inch  will  be  used.  Then,  the  intensity  of  shearing  stress 

at  the  end  is  =  6,180  pounds  per  square  inch;  and, 

as  the  shear  is  nearly  constant  from  the  truss  to  the  stringer, 
this  will  be  taken  as  the  intensity  of  shearing  stress  on  that 
portion  of  the  floorbeam.  Consulting  Table  XXXVI,  it  is 
seen  that  the  allowable  unsupported  distance  on  the  web  is 
33  inches.  The  vertical  legs  of  the  flange  angles  will  prob¬ 
ably  be  6  inches  wide,  leaving  the  distance  between  them 
30  inches;  as  this  is  less  than  the  allowable  distance,  no 
stiffeners  are  required. 

22.  Design  of  Flanges. — The  required  area  of  flange 
will  be  found  by  the  formula 

A  —  M  _  th 

s  hs  8 

The  value  of  hs  will  be  assumed  to  be  3  inches  less  than 
the  distance  back  to  back  of  the  flange  angles,  that  is,  42.25  —  3 
=  39.25  inches.  Then, 

a  769,500  X  12  42  X  i  o  oq 

A  ~  16,000  X  39.25  ~  ~ UJ°  ~  328 
=  11.42  square  inches. 

For  the  bottom  flange,  two  angles  6  in.  X  6  in.  X  in. 
will  be  used.  As  there  will  be  no  flange  plates  in  this  case, 
there  is  no  necessity  for  rivets  in  the  outstanding  legs  of  the 
bottom  flange  angles  at  the  point  where  the  moment  is 
greatest,  so  that  it  will  be  sufficient  to  deduct  the  cross-sec¬ 
tion  of  one  hole  from  each  angle.  The  area  of  one  angle  is 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  13 


6.43  square  inches  (Table  IX);  the  area  to  be  deducted  for 
one  i-inch  rivet  hole  in  material  t&  inch  thick  is  .56  square 
inch.  Then,  the  net  area  of  the  two  angles  is  2  (6.43  —  .56) 
=  11.74  square  inches,  which  is  sufficient.  The  center  of 
gravity  is  1.71  inches  from  the  back  of  the  angles. 

For  the  top  flange,  two  angles  6  in.  X  3i  in.  X  tw  in.  and 
one  flange  plate  8  in.  X  i  in.  will  be  used.  They  give  a 
gross  area  of  11.92  square  inches,  which  is  sufficient.  The 
center  of  gravity  is  1.28  inches  from  the  top  of  the  angles. 
This  gives  hs  =  42.25  —  1.71  —  1.28  =  39.26  inches,  which 
is  very  close  to  the  assumed  distance.  It  is  customary  to 
make  the  top  flange  of  the  floorbeam  as  narrow  as  practi¬ 


cable,  on  account  of  the  fact  that  it  projects  above  the  string¬ 
ers  and  therefore  lies  between  the  ties  (see^,  Fig.  5),  which 
must  be  spread  to  make  room  for  it. 

23.  Length  of  Flange  Plate. — The  required  length  of 
flange  plate  can  be  found  by  the  curve  of  the  flange  areas  for 
the  portion  of  the  floorbeam  between  the  truss  and  the 
stringer  (see  Design  of  Plate  Girders ,  Part  1).  This  curve  is 
shown  in  Fig.  9:  A  B  represents  the  distance  from  the  truss 

to  the  stringer,  B  D  the  required  area  B  B'  one-eighth 

KJ 

of  the  web  &  C  area  t^ie  two  Aan£e  angles,  and 

CD'  the  area  of  the  flange  plate.  As  the  bending  moment 
from  A  to  B ,  due  to  all  the  loads  except  the  weight  of  the 
floorbeam,  varies  uniformly  from  A  to  B ,  it  is  customary  to 


14  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


assume  that  the  curve  of  the  flange  areas  AD  is  a  straight 
line.  It  is  unnecessary  to  consider  the  required  flange  area 
between  the  stringers,  as  the  entire  flange  section  is  carried 
between  them. 

The  line  C  C  is  drawn  parallel  to  A  B ,  to  its  intersection  C 
with  A  D,  and  C  c  is  drawn  at  right  angles  to  A  B;  then,  c  is 
the  section  at  which  the  flange  plate  can  be  cut  off.  The 
distance  A  c  can  be  found  very  readily  by  the  formula 


A  c  = 


Oc 

BD 


XAB 


In  the  present  case,  C  c  —  3.28  +  7.92  =  11.20,  BD 
=  14.70,  and  A  B  —  4.75;  therefore,' 

A  c  =  x  4.75  =  3.62  feet 

24.  Flange  Rivets. — The  flange  rivets  are  i  inch  in 
diameter,  shop  driven,  in  double  shear,  and  in  bearing  on  the 
f-inch  web;  the  bearing  value,  12,000  pounds,  is  the  smaller. 
Since  the  flange  angles  are  42i  inches  back  to  back,  and  the 
center  line  between  the  gauge  lines  is  3f  inches  from  the 
back  of  the  angles  (Table  XII),  the  rivet  lines  of  the  flanges 
are  42.25  — 3.375  — 3.375  =  35.5  inches  center  to  center.  Then, 
(see  formula  in  Art.  13),  the  required  pitch  of  the  rivets  at 

the  end  of  the  floorbeam  is  =  2.63  inches. 

162,260 

As  the  shear  is  very  nearly  constant  from  the  truss  to  the 
stringer  connection,  this  pitch  will  be  used  for  that  entire 
distance.  The  shear  between  the  two  stringers  is  practi¬ 
cally  equal  to  zero,  so  that  the  smallest  allowable  pitch,  or 
4|  inches,  will  be  used  in  the  floorbeam  flanges  between 
them  ( B .  X.,  Art.  57). 

As  the  width  of  the  outstanding  leg  of  the  top  flange  angles 
is  3i  inches,  only  one  line  of  rivets  can  be  driven  in  it,  while 
in  the  vertical  leg,  6  inches  wide,  two  rows  can  be  driven. 
The  required  pitch  or  number  of  rivets  in  the  outstanding 
leg  in  this  case  can  be  found  by  considering  the  stress  in  the 
8"  X  flange  plate.  As  the  area  of  the  plate  is  4  square 
inches,  and  the  working  stress  in  compression  is  16,000 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  15 

pounds  per  square  inch  (B.  S.,  Art.  29),  the  total  stress 
in  the  plate  is  4  X  16,000  -  64,000  pounds.  The  value  of 
one  rivet  ( &  inch  in  diameter,  shop  driven,  in  single  shear)  is 
6,610  pounds.  Then,  the  number  of  rivets  required  to  trans¬ 
mit  the  stress  to  the  plate  is  =  9.7,  or,  say,  10.  That  is, 

6,610 

there  must  be  10  rivets  in  the  top  flange  plate,  between  the 
stringer  connection  and  the  end  of  the  plate.  If  it  is  impos¬ 
sible  to  get  this  number  of  rivets  in  the  distance  c  B,  Fig.  9, 
without  violating  the  rules  for  minimum  rivet  pitch,  the  top 
flange  plate  will  be  made  longer  than  required  by  the  curve 
of  flange  areas.  In  any  case,  it  is  well  to  make  it  slightly 
longer  than  required. 

25.  Connection  of  Floorbeam  to  Truss. — The  floor- 
beams  of  railroad  bridges,  especially  in  pin-connected  truss 
bridges,  are  frequently  connected  to  the  vertical  posts  above 
the  lower  chord  in  the  same  way  as  in  the  highway  bridge 
designed  in  the  two  preceding  Sections  of  this  Course.  A 
much  more  usual  connection,  however,  especially  for  riveted 
trusses,  is  shown  in  Fig.  10.  In  this  figure,  (a)  is  the  eleva¬ 
tion  of  one  end  of  the  floorbeam,  showing  the  holes  for  the 
stringer  connection  and  the  cross-section  of  the  bottom  chord 
of  the  truss,  together  with  the  elevation  of  a  vertical  post; 

( b )  is  an  end  view  of  the  connection  angles  of  the  floorbeam; 

( c )  is  a  cross-section  on  the  plane  C  C  and  a  plan  of  the  lower 
flange;  and  ( d )  is  a  top  view  of  a  portion  of  the  top  flange. 
The  stringer  connection  was  considered  in  Art.  14,  and  will 
not  be  further  discussed.  The  splice  in  the  floorbeam  web 
and  the  connection  to  the  truss  will  now  be  considered. 

26.  The  main  object  in  this  type  of  connection  is  to  dis¬ 
tribute  the  load  that  comes  from  the  floorbeam  over  a  greater 
length  of  the  vertical  member,  thereby  insuring  a  better  dis¬ 
tribution  of  the  load  between  the  two  sides  of  the  truss.  For 
this  purpose,  the  depth  of  the  floorbeam  web  is  increased  at 
the  end;  this  is  accomplished  by  splicing  the  web  between 
the  truss  and  the  stringer  at^,  and  allowing  a  portion  /  of  the 
end  of  the  web  to  project  up  through  the  top  flange  angles. 


V 


Fig.  10 


16 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  17 


The  deep  end  portion  of  the  web,  frequently  called  the  floor- 
beam  gusset,  should  not  come  inside  the  clearance  line,  as 
given  in  B.  S.,  Art.  18,  and  shown  at^  in  Fig.  10. 

It  is  not  customary,  in  splicing  a  floorbeam  web,  to  apply 
the  formulas  given  in  Design  of  Plate  Girders ,  Part  1,  but 
rather  to  design  the  splice  so  as  to  transmit  the  shear  from 
one  portion  of  the  web  to  the  other.  As  a  rule,  if  the  floor- 
beam  is  over  3  feet  deep,  and  each  splice  plate  h  is  made  the 
same  thickness  as  the  web,  and  three  rows  of  rivets  spaced 
3  inches  apart,  as  shown  in  Fig.  10,  are  put  in  on  each  side  of 
the  splice,  it  will  be  unnecessary  to  make  any  computation. 
When  the  floorbeam  is  less  than  3  feet  deep,  the  splice  plates 
are  turned  into  reinforcing  plates  and  continued  from  the  end 
of  the  floorbeam  out  beyond  the  splice  and  stringer  connec¬ 
tion.  In  the  splice  shown  in  Fig.  10,  the  resisting  moment 
of  the  rivets  is  not  so  great  as  that  of  the  web,  but  at  this 
section  there  is  sufficient  flange  area  even  if  the  effect  of  the 
web  in  resisting  the  moment  is  not  counted;  so  that  it  is  not 
necessary  to  have  the  resisting  moment  of  the  rivets  so  great 
as  that  of  the  web  at  this  section. 

The  rivets  connecting  the  connection  angles  i  to  the  gusset 
are  t  inch  in  diameter,  and  shop  driven.  Their  smallest 
value  is  that  in  bearing  on  the  i-inch  gusset,  and  is 
12,000  pounds.  Since  the  end  shear  on  the  floorbeam  is 


162,260  pounds,  the  number  of  rivets  required  is 


162,260 


12,000 

=  13.5,  or,  say,  14.  The  rivets  connecting  the  connection 
angles  to  the  truss  are  field  driven;  their  value  in  single 
shear,  5,410  pounds,  is  the  smallest.  The  required  number 

of  rivets  is  --■■■*—  =  30. 

5,410 

In  Fig.  10,  there  are  more  rivets  than  are  necessary.  This 
is  a  common  practice,  as  it  is  considered  advisable  to  have  a 
few  extra  rivets. 


27.  No  rule  can  be  given  as  to  the  height  of  the  floor- 
beam  gusset  at  the  end.  In  half-through  plate-girder  bridges, 
the  gusset  is  continued  up  to  the  under  side  of  the  top  flange; 


18  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


in  pony-  truss  bridges,  it  is  made  as  large  and  as  high  as  the 
clearance  line  will  allow;  in  through  truss  bridges,  as  in  the 
present  case,  its  height  depends  on  the  depth  of  the  floor- 
beam  and  somewhat  on  the  required  number  of  rivets  in 
the  connection  angle.  In  no  case  should  the  gusset  encroach 
on  the  required  clearance. 

The  gusset  is  cut  near  the  bottom  at  j  to  allow  for  the  out¬ 
standing  leg  of  the  top  flange  angle  of  the  bottom  chord, 
and  the  connection  angle  i  on  each  side  is  put  on  in  two 
pieces.  The  connection  angles  will  be  made  4  in.  X  4  in. 
X  I  in. 

28.  Between  the  bottom  of  the  floorbeam  and  the  top 
side  of  the  outstanding  leg  of  the  lower  flange  angle  of  the 
bottom  chord  is  placed  a  plate  k ,  i  inch  thick,  which  is 
riveted  to  the  chord  and  to  the  bottom  flange  of  the  floor- 
beam,  and  serves  the  purpose  of  connecting  the  diagonals  of 
the  lateral  truss  to  the  floorbeam  and  bottom  chord.  The 
lateral  connections  will  be  discussed  further  on. 

29.  In  Fig.  5,  the  distance  from  the  base  of  the  rail  to 
the  top  of  the  stringer  is  7}  inches  (B.  S .,  Art.  48),  and  the 
top  of  the  shelf  angle  is  6f  inches  above  the  bottom  of  the 
bottom  flange  of  the  floorbeam,  making  the  bottom  of 
the  floorbeam  3  feet  8i  inches  below  the  base  of  the  rail. 
Adding  to  this  2  inch  for  the  thickness  of  the  lateral  con¬ 
nection  plate  k ,  and  f  inch  for  the  thickness  of  the  bottom 
chord  angle  l  (to  be  found  later),  gives  the  distance  from 
the  base  of  the  rail  to  the  bottom  of  the  bottom  chord  as 
3  feet  9f  inches,  as  shown  in  Fig.  10.  This  distance  will  be 
referred  to  again  in  the  following  articles. 


END  STRUTS  OR  FRAMES 

30.  For  the  sake  of  variety,  no  end  floorbeams  will  be 
provided,  although  in  the  best  practice  they  are  always  put 
in.  In  the  present  case,  the  end  stringers  will  be  allowed  to 
rest  directly  on  the  masonry,  and  their  ends  will  be  connected 
to  each  other  and  to  the  ends  of  the  trusses  by  frames,  as 


Base  of  Ra/7 


I 


§  7<)  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  1!) 


20  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


shown  in  Fig.  11.  Four  stiffeners  are  placed  at  the  end  of 
each  stringer  where  it  rests  on  the  masonry,  and  sole  plates 
and  bedplates  1  inch  thick  are  provided,  as  shown  in  Fig.  12. 
In  the  present  case,  the  bedplates  will  be  made  20  inches 
square,  which  is  a  customary  size.  It  is  unnecessary  to  calcu¬ 
late  the  required  thickness  of  the  end  stiffeners  on  stringers; 
if  the  smallest  allowable  angles  are  used — in  the  present 
case,  5  in.  X  3i  in.  xt  in.  (B.  S.,  Art.  55) — they  will  be  large 
enough.  End  stringers  are  usually  made  somewhat  longer 
than  the  intermediate  stringers;  the  difference  is  equal  to 
one-half  the  length  of  the  bedplate,  which  makes  the  distance 
from  the  center  of  the  bedplate  to  the  next  floorbeam  equal 


to  a  panel  length.  Otherwise,  the  end  stringers  are  the 
same  as  the  intermediate  stringers.  As  shown  in  Fig.  11, 
end  frames  are  usually  made  shallower  than  the  stringers. 
The  tops  of  the  frames  are  placed  below  the  tops  of  the 
stringers  that  the  frames  may  not  interfere  with  the  ties. 
The  bottoms  of  the  frames  are  placed  above  the  bottoms 
of  the  stringers  so  as  to  have  the  former  above  the  bridge 
seat. 

The  connection  of  the  outside  frames  b)  b,  Fig.  11,  to  the 
trusses  will  be  considered  later. 


§  79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


21 


DESIGN  OF  TRUSSES 


STRESSES 

31.  Instead  of  finding  the  actual  stresses  caused  in  the 
different  members  by  the  different  loadings,  as  in  Stresses  in 
Bridge  Trusses ,  Part  2,  the  shears  and  moments  will  be  found, 
and,  after  properly  combining  them,  the  stresses  will  be  cal¬ 
culated. 


32.  Eive-Eoad  Shears  and  Moments. —The  portion 
of  the  live  load  that  goes  to  each  truss  is  one-half  of  Cooper’s 
E50,  as  shown  in  Fig.  2.  The  portion  that  the  load  must 
occupy  in  order  to  cause  the  greatest  shear  in  a  panel  or 
the  greatest  moment  at  a  panel  point  is  found  by  means  of  the 
principles  explained  in  Stresses  in  Bridge  Trusses ,  Part  4.  The 
maximum  positive  live-load  shears  in  the  different  panels, 
and  the  corresponding  positions  of  the  loads,  are  as  follows 
(see  Fig.  13): 


Panel 

Position  of  Load 

Maximum  Positive  Shear 
Pounds 

a  b 

3  at  b 

207,850 

b  c 

3  at  c 

156,910 

c  d 

3  at  d 

1 1 1,400 

d  e 

2  at  e 

72,220 

e  df 

2  at  d' 

42,570 

d'c' 

2  at  cf 

20,310 

c'b ' 

i  at  bf 

4,170 

The  maximum  live-load  bending  moments  at  the  different 
panel  points,  and  the  corresponding  positions  of  the  loads, 
are  as  follows: 


135—19 


22  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


Panel  Point 

Position  of  Load 

Maximum  Bending  Moment 
Foot-Pounds 

b 

3  at  b 

3>74L300 

c 

5  at  c 

6,180,000 

d 

8  at  d 

7,57L9oo 

c 

1 1  at  e 

8,165,600 

33.  Impact  and  Vibration. — The  amount  to  be  added 
to  each  shear  and  bending  moment  found  above  to  allow  for 
the  effect  of  impact  and  vibration  depends  on  the  length  L  of 
the  track  that  is  loaded  when  the  shear  or  moment  is  a  max¬ 
imum.  When  load  1  is  off  the  left  end,  the  entire  bridge  is 
loaded,  and  L  is  144  feet;  when  load  1  is  on  the  bridge,  L  is 
the  distance  from  the  right  end  to  load  1.  For  example, 


when  the  shear  in  the  panel  c  d  is  a  maximum,  load  3  is  at  d; 
in  this  case,  since  load  1  is  13  feet  to  the  left  of  d,  and  d  is 
90  feet  to  the  left  of  the  right  end  of  the  truss,  load  1  is  13  +  90 
=  103  feet  from  the  right  end;  that  is,  L  =  103  feet.  Apply¬ 


ing  the  formula  given  in  B.  S.,  Art.  25  ( I  —  — gives 

\  L  +  300/ 

the  amounts  to  be  added  to  the  shears  and  bending  moments 
as  follows: 


Panel 

a  b 

I  = 

b  c 

/  = 

c  d 

/  = 

Shear,  in  Pounds 

is ifs»  *  207-0”  -  142-°“ 
iiSs  x  15e'*“  -  nim 

wfmxnhm-  82-900 


§  TO  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  28 


Panel 
d  e 

e  df 

d'c ' 

c'b' 

Panel 

Point 


I  = 


/  = 


Shear,  in  Pounds 

X  72,200  =  57,000 


/  = 


/  = 


80  +  300 
300 

62  +  300 
300 

44  +  300 
300 


X  42,600  =  35,300 
X  20,300  =  17,700 

18  +  300  X  4’17°=  3’93° 
Bending  Moment,  in  Foot-Pounds 


*  7  -  BsSoo  x  8'741'300  -  2’556’™ 

*  /=  -1313°°300  X  6,180,000  =  4,301,700 

'  7  -  ibSoo  x  7-571-”0  - 

'  7  '  mVSxi x  8'165’600  -  5'618'M0 


34.  Dead-Load  Shears  and  Moments. — The  dead 
load  consists  of  the  weight  of  the  track  and  the  weight  of 
the  bridge.  In  the  general  data,  it  is  stated  that  the  floor 
shall  consist  of  standard  ties,  and  in  B.  S.,  Art.  23,  it  is 
specified  that  this  type  of  floor  shall  be  assumed  to  weigh 
400  pounds  per  linear  foot.  The  approximate  weight  wx  per 
linear  foot  of  bridge  can  be  found  by  means  of  the  formula 


given  in  B. 
therefore, 

wx  =  1,500 


S.,  Art.  242.  In  the  present  case,  /  =  144; 


1,937.4  lb.  per  linear  foot 


The  total  dead  load  per  linear  foot  is,  therefore,  400 
+  1,937.4  =  2,337.4  pounds,  of  which  one-half,  or  1,168.7 
pounds  per  linear  foot,  goes  to  each  truss.  The  dead 
panel  load  is  equal  to  1,168.7  X  18  =  21,036.6  pounds,  or, 
practically,  21,000  pounds;  of  this  load,  one-third,  or 
7,000  pounds,  will  be  treated  as  applied  at  each  top  joint, 
and  the  remainder,  14,000  pounds,  as  applied  at  each  lower 
joint  of  the  truss.  (B.  S.t  Art.  23.) 


24 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


The  dead-load  shears  in  the  different  panels  are  then  as 
follows  (see  Fig.  13): 


Panel 
a  b 
be 
cd 
de 
ed ' 
d'e' 
c'b ' 
Vat 


Shear,  in  Pounds 

73.500  (positive) 

52.500  (positive) 

31.500  (positive) 

10.500  (positive) 

10.500  (negative) 

31.500  (negative) 

52.500  (negative) 

73.500  (negative) 


The  dead-load  bending  moments  at  the  different  panel 
points  are  as  follows: 


Panel 

Point 

b 

c 

d 

e 


Bending  Moment, 
in  Foot-Pounds 

1,323,000 

2,268,000 

2,835,000 

3,024,000 


35.  Increase  in  Shears  and  Moments  on  Account 
of  Wind  Pressure  on  tlie  Train. — The  load  on  the 
leeward  truss  is  increased  by  the  overturning  effect  of  the 
wind.  The  amount  of  the  increase  can  be  found  by  the  fol¬ 
lowing  formula,  given  in  Stresses  in  Bridge  Trusses ,  Part  5: 


w 


Ph 

b 


In  this  formula,  P  is  the  intensity  of  wind  pressure, 
300  pounds  per  linear  foot  ( B .  A.,  Art.  27);  1v  is  the  dis¬ 
tance  from  the  center  of  wind  pressure  to  the  lower  lateral 
system,  and  will  be  taken  as  11.25  feet  (see  Fig.  10);  b  is 
the  distance  center  to  center  of  trusses,  in  this  case  16  feet. 
Then, 


w 


300  X  11.25 
16 


210.94  pounds  per  linear  foot 


The  increase  in  the  panel  loads  is  then  210.94  X  18 
—  3,797,  or,  practically,  3,800  pounds.  The  shears  due  to 
this  increase  are  as  follows: 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  25 


Panel 

Positive  Shear, 
in  Pounds 

a  b 

13,300 

be 

9,975 

cd 

7,125 

de 

4,750 

ed' 

2,850 

d'e' 

1,425 

c'  bf 

475 

The  bending  moments  due  to  this  increase  are  as  follows: 

Panel  Bending  Moment, 

Point  in  Foot-Pounds 

b  239,400 

c  410,400 

d  513,000 

e  547,200 

Those  stresses  to  which  the  members  are  subjected  as 
members  of  the  lateral  trusses  will  be  considered  later,  and 
treated  in  the  same  way  as  for  highway  bridges. 

36.  Longitudinal  Force. — The  longitudinal  force  due 
to  suddenly  stopping  trains  is  taken  care  of  by  connecting 
the  stringers  to  the  diagonals  of  the  lower  lateral  truss  wher* 
ever  they  intersect.  No  calculations  are  needed  for  this 
connection;  it  is  made  in  the  most  convenient  way.  The 
laterals  transmit  the  force  to  the  trusses,  which  in  turn 
transmit  it  to  the  abutments. 


37.  Combined  Maximum  Shears  and  Moments.- 
The  combined  maximum  shears  are  as  follows: 


Panel 

Combined  Maximum  Shear,  in 

Pounds 

a  b 

207,800 

4* 

142,000 

+ 

73,500 

+ 

13,300 

=  436,600 

be 

156,900 

+ 

111,800 

+ 

52,500 

+  : 

10,000 

=  331,200 

c  d 

111,400 

+ 

82,900 

+ 

31,500 

+ 

7,100 

=  232,900 

de 

72,200 

+ 

57,000 

+ 

10,500 

+ 

4,700 

=  144,400 

ed' 

42,600 

+ 

35,300 

— 

10,500 

+ 

2,800 

70,200 

d'e' 

20,300 

+ 

17,700 

— 

31,500 

4" 

1,400 

=  7,900 

c'b' 

4,200 

+ 

3,900 

— 

52,500 

+ 

500 

=  -  43,900 

Since  the  combined  shears  in  the  panels  ed'  and  d'  cf  are 
positive,  counters  are  required  in  these  two  panels.  Since 


20 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


the  combined  shear  in  the  panel  c'  bf  is  negative,  no  counter 
is  required  in  this  panel. 

The  combined  maximum  bending  moments  are  as  follows: 

Panel  Combined  Maximum  Bending  Moment, 

Point  in  Foot-Pounds 

b  3,741,300  +  2,556,700+1,323,000+239,400  =  7,860,400 

if  6,180,000+4,301,700  +  2,268,000  +  410,400  =  13,160,100 

d  7,571,900+5,246,100  +  2,835,000  +  513,000  =  16,166,Q00 

e  8,165,600+5,618,500+3,024,000  +  547,200  =  17,355,300 


38.  Stresses  in  the  Members. — Since  the  depth  of  the 
truss  is  26.5  feet,  the  maximum  chord  stresses,  to  the  nearest 
100  pounds,  are  as  follows: 

Member  Stress,  in  Pounds 

a  by  be  =  296,600  (tension) 

c  d  13’26°5100  =  496>600  (tension) 

dc  16,166  000  =  610>000  (tension) 

Zo.b 

BC  496,600  (compression) 

CD  610,000  (compression) 

D E  17^355^00  _  054 ,900  (compression) 

Zu  .0 

The  length  of  the  diagonal  is  V26.-5*  +  182  =  32.035  feet, 
32.035  _  2  209.  Then,  the  stresses  in  the  diag- 


and  esc  H  = 


26.5 


onals  are  practically  as  follows: 


Diagonal 
a  B 
Be 
Cd 
De 

Ed'  or  d E 
D’  c'  or  c  D 


Stress,  in  Pounds 

436,600  X  1.209  =  527,800  (compression) 
331,200  X  1.209  =  400,400  (tension) 
232,900  X  1.209  =  281,600  (tension) 
144,400  X  1.209  =  174,600  (tension) 
70,200  X  1.209  =  84,900  (tension) 

7,900  X  1.209  =  9,600  (tension) 


The  stress  in  the  hip  vertical  is  equal  to  the  end  shear  on 
the  floorbeam,  which  is  162,300  pounds.  Then,  the  stress 
in  B  b  is  162,300  pounds,  tension. 


§  79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


27 


The  stresses  in  the  other  verticals  are  as  follows: 


Member 

Cc 

Dd 

Ee 


Compressive  Stress, 
in  Pounds 

232,900  +  7,000  =  239,900 
144,400  +  7,000  =  151,400 
70,200  +  7,000  =  77,200 


The  above  combined  stresses  are  shown  on  the  members 
in  Fig.  14.  _ 


DESIGN  OF  MEMBERS 

39.  Bottom  Chord.— Since  the  working  stress  in  ten¬ 
sion  is  16,000  pounds  per  square  inch,  the  required  net  areas 
of  the  bottom  chord  members  are  as  follows: 


Member 

Required  Net  Area, 
in  Square  Inches 

a  by  be 

296,60(1  =  lg  g4 
16,000 

cd 

496,600  _  31  04 
16,000 

de 

i 

610,000  ,q  jo 

16,000 

Fig.  15  shows  the  usual  type  of  member  used  for  the 
bottom  chords  of  riveted  trusses.  It  consists  of  two  vertical 
webs  c ,  four  flange  angles  d ,  and,  when  necessary,  two  side 
plates  e.  The  two  sides  of  the  section  are  connected  by 
double  latticing  /  at  the  top  and  bottom.  The  customary 
method  of  riveting  the  parts  of  the  section  together  is  shown 
in  the  figure.  In  computing  the  net  section,  allowance  must 


28  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


be  made  for  the  greatest  number  of  rivet  holes  in  each  part 
of  the  section.  The  rivets  are  i  inch  in  diameter. 

The  usual  depth  of  this  type  of  member  varies  from  about 
12  to  24  inches;  in  the  present  case,  it  will  be  made  15  inches. 


(b) 

The  clear  width  between  the  webs  depends  on  the  width 
of  the  web  members  and  other  details,  and  is  generally  from 
12  to  24  inches. 

40.  Design  of  Bottom  Chord  Members. — 1.  Mem - 
bers  ab  a?id  be  (Fig.  14). — The  bottom  chord  will  be  spliced 
in  panels  cd  and  d'  c'  close  to  the  joints  d  and  d\  so  that  the 
parts  that  form  a  b  and  b  c  will  also  form  part  of  c  d .  The  fol-  * 
lowing  shapes  will  be  used  for  ab  and  be: 

2  web  plates  15  in.  X  I  in. 

4  angles  3i  in.  X  3|-  in.  X  I  in. 

Three  holes  must  be  deducted  from  each  web,  and  one  hole 
from  each  angle;  then,  the  net  area  of  the  section  is  as 
follows: 

2  plates  15  in.  X  I  in.,  net  section 

=  2  (5.625  —  3  X  .375)  .  .  .  =  9.0  square  inches 

4  angles  3i  in.  X  3h  in.  X  t  in.,  net 

section  —  4  (3.98  — .625)  .  .  =  13.42  square  inches 

Total  net  section  .  .  =  22.42  square  inches 

This  is  somewhat  more  than  necessary,  but  it  is  desirable 
to  use  these  sizes  in  the  present  case,  because,  by  the  addi¬ 
tion  of  two  side  plates  of  about  the  same  thickness  as  the 
angles,  the  next  member  cd  can  be  formed. 

2.  Member  cd. — As  the  web  is  15  inches  deep  and  the 
flange  angles  are  3i  inches  in  width,  the  side  plates  will  be 
made  8  inches  in  width,  and  two  rivet  holes  will  be  deducted 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  29 


from  each  plate.  The  net  area  of  two  plates  8  in.  X  t  in.  is 
2  (6.0  —  2  X  .75)  =  9.0  square  inches;  this,  added  to  the  net 
area  of  ab  and  be,  gives  9.0  +  22.42  =  31.42  square  inches, 
which  is  sufficient. 

3.  Member  de. — The  same  general  form  will  be  used  as 
for  c  d,  except  that  the  webs  will  be  made  f  inch  thick  instead 
of  f  inch.  Then,  the  net  area  is  as  follows: 

2  plates  15  in.  X  1  in.,  net  area 

=  2  (11.25  —  3  X  .75)  .  .  =  18.0  square  inches 
4  angles  3i  in.  X  3|  in.  X  t  in., 

net  area  =  4(3.98  —  .625)  =  13.42  square  inches 
2  plates  8  in.  X  f  in.,  net  area 

=  2  (5.0  —  2  X  .625)  .  .  =  7.50  square  inches 


Total  net  area  .  .  =  38.92  square  inches 


41.  Location  of  Center  Line  of  Bottom  Chord. 
The  center  line  of  the  bottom  chord  will  be  placed  a  short 
distance  above  the  center  of  gravity  of  the  section,  so  that 
the  bending  moment  caused  in  the  chord  members  by  the 
eccentricity  of  the  stress  will  neutralize  that  due  to  the  weight 
of  each  member  considered  as  a  beam  having  a  span  equal 
to  a  panel  length.  The  eccentricity  will  be  found  for  the 
heaviest  member  (de),  and  will  be  made  the  same  for  all  the 
bottom  chord  members.  The  gross  area  of  de  is  48.4  square 
inches,  and  this  member  weighs  161  pounds  per  linear  foot. 
To  allow  for  the  weight  of  latticing,  the  weight  will  be  taken 
about  10  per  cent,  greater,  or,  say,  17.5  pounds  per  linear  foot. 
The  required  eccentricity^,  in  inches,  is  computed  by  the  fol¬ 
lowing  formula,  given  in  Bridge  Members  and  Details,  Part  1: 

w  r 


e  = 


8  ^ 


X  12 


In  the  present  case,  w  =  175,  l  =  18,  and  6*  =  610,000 
(Art.  38);.  therefore, 

_  175  X  18  y  =  .14  inch,  or,  say,  i  inch 

8X610,000 

Then,  as  the  center  of  gravity  is  7f  inches  from  the  bottom 
of  the  angles,  the  center  line  will  be  7f  +  i  =  7f  inches 
above  the  bottom  of  the  bottom  angles. 


30  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


42.  Main  Diagonals  and  Counters. — In  this  article, 
only  the  tension  diagonals  will  be  designed;  the  design  of 
the  end  post  will  be  considered  in  connection  with  the  design 
of  the  top  chord.  The  required  net  areas  are  as  follows: 


Member 

Required  Net  Area 
in  Square  Inches 

Be 

400,400  =  25  02 
16,000 

cd 

281,600  =  17  60 
16,000 

De 

174,600  =  10  91 
16,000 

dE 

84,900  =  5gl 
16,000 

cD 

9,600  =  g0 

16,000 

For  members  requiring  more  than  about  15  square  inches 
net  area,  the  form  of  cross-section  most  frequently  used  is 


/Q)(Q\ 


m m  if 


\QVQ/ 


\QXQ/ 


Fig.  16 


lb 


1  -It- 


i  i r 


Fig.  17 

the  same  as  that  of  the  bottom  chord  members  that  have  just 
been  considered.  For  the  others,  either  two  or  four  angles 
latticed  together  as  shown  in  Figs.  16  and  17  are  used. 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  31 


1.  Member  Be . — Where  the  diagonals  are  riveted  to  the 
connection  plates,  the  web  will  be  reduced  by  three  i-inch 
rivet  holes,  and  each  angle  by  one  rivet  hole.  The  follow¬ 
ing  section  will  be  used  for  this  member: 

Square 

Inches 

2  plates  15  in.  X  i  in.,  net  area  =  2(7.5  —  3  X  .5)  =  12.00 

4  angles  3i  in.  X  3i  in.  xf  in.,  net  area  =  4(3.98  — .625)  =  13.42 

i  - — 

Total  net  area  =  25.42 

2.  Member  Cd. — The  following  section  will  be  used  for 
this  member: 

Square 

Inches 

2  plates  14  in.  X  i  in.,  net  area  =  2(7.0  —  3  X  .5)  =  11.00 

4  angles  3  in.  X  3  in.  X  t  in., net  area  =  4(2.11  —  .375)  =  6.94 

Total  net  area  =  17.94 

3.  Member  De. — As  the  required  net  area  is  less  than 
15  square  inches,  this  member  will  be  composed  of  four 
angles.  The  section  of  each  angle  will  be  decreased  by  one 
1-inch  rivet  hole.  The  following  section  will  be  used  for 
this  member: 

4  angles  4  in.  X  3  in.  X  2  in.,  net  area  =  4  (3.25  —  .5) 

=  11  square  inches 

4.  Member  d E. — This  member  is  a  counter,  and  the  same 
type  of  member  will  be  used  as  for  D  <?,  except  that  only  two 
angles  are  needed,  as  follows: 

2  angles  4  in.  X  3  in.  X  2  in.,  net  area  =  2  (3.25  —  .5) 

=  5.50  square  inches 

5.  Member  cD. — This  member  is  also  a  counter,  the 
required  net  section  of  which  is  .60  square  inch.  According 
to  B.  S.,  Art.  69,  the  net  area  cannot  be  less  than  3  square 
inches,  and  if  two  of  the  smallest  allowable  angles  are  used 
(3  in.  X  3  in.  X  I  in.,  B.  S.f  Art.  39),  the  net  area  will 
be  2  (2.11  —  .375)  =  3.47  square  inches.  This  is  the  smallest 
section  that  can  be  used,  and  will  be  adopted. 

43.  Compression  Verticals. — The  most  desirable  sec¬ 
tion  for  the  verticals  consists  of  two  channels  with  their 
flanges  turned  toward  each  other  and  connected  by  latticing  /, 


32  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


Fig.  18.  The  easiest  way  to  find  the  proper  sections  is  to 
begin  at  the  center  of  the  truss  and  work  toward  the  end, 
trying  the  smallest  allowable  sections  at  the  center,  and 
increasing  them  toward  the  end.  The  length  of  a  vertical 
from  center  to  center  of  chords  is  26.5  feet,  or  318  inches. 


In  B.  S.f  Art.  32,  it  is  specified  that  the  ratio  of  the  length  to 
the  least  radius  of  gyration  shall  not  exceed  100,  from  which 
it  may  be  seen  that  in  the  present  case  the  least  allowable 

318 

value  of  the  radius  of  gyration  is  - —  =  3.18  inches.  If  the 

100 

channels  are  placed  far  enough  apart,  only  the  radius  of 
gyration  about  an  axis  at  right  angles  to  the  web  need  be 
considered. 

1.  Member  Ee  (Fig.  14). — Consulting  Table  XIII,  it  is 
seen  that  the  smallest  channel  having  a  radius  of  gyration  as 
great  as  3.18  inches  is  a  9-inch  13.25-pound  channel;  but  this 
cannot  be  used,  as  its  web  is  less  than  f  inch  in  thickness 
( B .  S.,  Art.  38).  The  lightest  channel  that  has  the  required 
thickness  is  a  9-inch  20-pound  channel,  and  this  might  be 
used.  A  10-inch  20-pound  channel,  however,  also  has  the 
required  value  of  radius  of  gyration  and  the  required  thick¬ 
ness,  and  as  it  is  not  heavier  and  is  somewhat  stifler  than 
the  9-inch  channel,  the  10-inch  20-pound  channel  will  be 
tried.  Its  radius  of  gyration  is  3.66  inches,  and,  therefore, 

-  =  =  86.9.  The  working  stress  (Table  XXXV)  is 

r  3.66 

11,270  pounds  per  square  inch.  Since  the  area  of  one 
channel  is  5.88  square  inches,  the  total  allowable  stress  on 
the  member  is  2  X  5.88  X  11,270  =  132,500  pounds,  com¬ 
pression.  As  this  is  greater  than  the  stress  in  Ee ,  two 
10-inch  20-pound  channels  will  be  used. 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  33 


2.  Member  Dd. — As  the  allowable  stress  in  two  10-inch 
20-pound  channels  is  less  than  the  actual  total  stress  in  D  d, 
it  is  necessary  to  use  a  heavier  section  for  this  member. 
The  next  size  of  channel  is  a  10-inch  25-pound  channel,  but  it 
is  better  to  use  a  12-inch  25-pound  channel,  which  is  somewhat 
stiffer  and  no  heavier.  The  radius  of  gyration  of  the  latter 

channel  is  4.43  inches,  and  -  =  — —  =  71.8.  The  working 

r  4.43 

stress  (Table  XXXV)  is  12,440  pounds  per  square  inch. 
Since  the  area  of  one  channel  is  7.35  square  inches,  the 
total  allowable  stress  on  the  member  is  2  X  7.35  X  12,440 
=  182,900  pounds,  compression.  As  this  is  greater  than 
the  stress  in  Dd,  two  12-inch  25-pound  channels  will  be  used 
for  this  member. 

3.  Member  Cc. — As  the  allowable  stress  in  two  12-inch  25- 

pound  channels  is  less  than  the  actual  total  stress  in  Cc,  it  is 
necessary  to  use  a  heavier  section  for  this  member.  The 
next  size  of  channel  is  a  12-inch  30-pound  channel;  but  it  is 
found  by  trial  as  above  that  this  is  not  large  enough.  Two 
15-inch  33-pound  channels  will  be  tried.  The  radius  of  gyra¬ 
tion  is  5.62  inches,  and  —  =  =  56.6.  The  working 

r  5.62 

stress  (Table  XXXV)  is  13,580  pounds  per  square  inch. 
Since  the  area  of  one  channel  is  9.90  square  inches,  the 
total  allowable  stress  on  the  member  is  2  X  9.90  X  13,580 
=  268,900  pounds,  compression.  As  this  is  greater  than 
the  stress  in  Cc,  two  15-inch  33-pound  channels  will  be  used. 

In  order  that  the  radius  of  gyration  with  reference  to  an 
axis  parallel  to  the  webs  shall  be  at  least  equal  to  that  about 
the  axis  at  right  angles  to  the  web,  the  channels  in  all  these 
verticals  must  be- +  4x  back  to  back  (see  Desigri  of  a 
Highway  Truss  Bridge ,  Part  1),  or,  in  this  case,  for  member 
Cc,  9.50  +  4  X  .79  =  12.66  inches.  The  actual  distance 
depends  on  other  details,  but  it  will  be  well  in  the  present 
case  to  make  it  from  12  to  13  inches. 

44.  Hip  Vertical. — The  same  form  of  cross-section 
will  be  used  for  this  member  as  for  the  other  verticals. 


34  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 
Since  the  stress  is  tension,  the  required  net  area  is 

16,000 

=  10.14  square  inches.  Two  i-inch  rivet  holes  will  be 
deducted  from  the  web  of  each  channel.  Two  10-inch  20- 
pound  channels  will  be  used.  Since  the  thickness  of  the 
web  is  .38  inch,  the  area  to  be  deducted  for  each  hole 
is  .38  square  inch.  Since  the  gross  area  of  one  channel 
is  5.88  square  inches,  the  net  area  of  two  channels  is 
2(5.88  —  2  X  .38)  =  10.24  square  inches,  which  is  sufficient. 

45.  Top  Chord.— The  cross-section  usually  employed 
for  top  chord  members  of  riveted  trusses  is  shown  in  Fig.  19. 
It  consists  of  a  top  cover-plate  a ,  two  web-plates  b ,  four 
flange  angles  c ,  and,  when  necessary,  two  side  plates  d. 

The  angles  are  connected  at 
the  bottom  by  latticing  /.  The 
top  chord  will  be  spliced  in  the 
panels  CD  and  D'  O  (Figs.  13 
and  14),  close  to  points  D  and 
D\  respectively,  so  that  the 
parts  that  make  up  B  C  will  con¬ 
tinue  beyond  C  and  form  part 
of  CD.  As  the  width  of  the 
web  members  is  about  13  inches, 
the  clear  distance  between  the 
webs  of  the  top  chord  will  be  assumed  as  14  inches,  leaving 
about  2  inch  on  each  side  for  gussets.  The  same  depth  of 
web  will  be  used  as  for  the  bottom  chord,  that  is,  15  inches. 
As  explained  in  Bridge  Members  and  Details ,  when  the  clear 
distance  between  the  webs  of  this  form  of  section  is  greater 
than  three-quarters  of  the  width  of  the  web,  as  in  this  case, 
the  radius  of  gyration  with  respect  to  an  axis  parallel  to  the 
webs  need  not  be  considered,  as  that  referred  to  an  axis  at 
right  angles  to  the  web  will  always  be  less. 

1.  Member  B  C. — The  general  method  of  arriving  at  the 
section  of  a  top  chord  member  by  trial  was  treated  at  length 
in  Design  of  a  Highway  Truss  Bridge ,  and  need  not  be 
repeated  here. 


a 


Fig.  19 


§  70  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


The  following  section  will  be  used  for  this  member: 

Gross  Area, 
in  Square  Inches 


1  cover-plate  22  in.  X  i  in.  1  1.0  0 

2  top  flange  angles  3f  in.  X  3f  in.  X  tV  in.  5.7  4 

2  web-plates  15  in.  X  fin.  1  1.2  5 

2  bottom  flange  angles  3i  in.  X  3|  in.  X  Te  in. _ 5.7  4 

Total  gross  area  =  3  3.7  3 


The  center  of  gravity  of  this  section  is  5.06  inches  from 
the  top  of  the  top  flange  angles,  and  10.19  inches  from  the 
bottom  of  the  bottom  flange  angles,  as  shown  in  Fig.  20. 
The  radius  of  gyration  with 
reference  to  an  axis  at  right 
angles  to  the  webs  and 
passing  through  the  center 
of  gravity  is  5.92  inches; 

-  =  =  36.5,  and  the 

r  5.92 

working  stress  (Table 
XXXV)  is  14,900  pounds 
per  square  inch.  Then, 
since  the  total  stress  in  this,  member  is  496,600  pounds, 

the  required  area  of  cross-section  is  —  33.33  square 

14,900 

inches.  As  the  gross  area  of  the  section  tried  above  is 

greater  than  the  required 
gross  area,  that  section  is 
sufficient,  and  will  be  used. 

2.  Member  CD. —  The 
same  simple  shapes  that 
were  used  for  B  C  will  be 
used  for  CD,  and,  in  addi¬ 
tion,  two  side  plates  8  in. 
X  2  in.  The  gross  area 
of  these  two  plates  is 
8  square  inches,  which,  added  to  the  area  of  B  C ,  gives 
8  +  33.73  =  41.73  square  inches,  gross  area  of  CD.  The 
center  of  gravity  of  this  section  is  5.55  inches  from  the  top  of 


Fig.  21 


Fig.  20 


36  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


the  top  flange  angles  and  9.70  inches  from  the  bottom  of  the 
bottom  flange  angles,  as  shown  in  Fig.  21.  The  radius 
of  gyration  with  reference  to  an  axis  at  right  angles  to 
the  webs  and  passing  through  the  center  of  gravity  is 

5.51  inches;  -  =  =  39.2,  and  the  working  stress 

r  5.51 

(Table  XXXV)  is  14,740  pounds  per  square  inch.  Then, 
since  the  total  stress*  is  610,000  pounds,  the  required  area 

of  cross-section  is  ==  41.38  square  inches.  As  the 

14,740 

section  tried  has  a  gross  area  greater  than  the  required  gross 
area,  it  will  be  used. 

3.  Member  D  E. — As  the  top  chord  will  be  spliced  near 
the  joint  D ,  different  shapes  can  be  used  from  those  used 
in  CD ,  but  it  is  advisable  to  adopt  the  same  width  of  top 
plate,  depth  of  web,  and  width  of  legs  of  angles,  although 
different  thicknesses  may  be  used.  The  following  sections 
will  be  tried  for  this  member: 

Gross  Area, 
in  Square  Inches 


1  cover-plate  22  in.  X  i^in.  1  2.3  8 

2  top  flange  angles  3^  in.  X  3|  in.  X  i  in.  6.5  0 

2  web-plates  15  in.  X  fin.  1  1.2  5 

2  side  plates  8  in.  X  i  in.  8.0  0 

2  bottom  flange  angles  3i  in.  X  in.  X  i  in.  6.5  0 

Total  gross  area  =  4  4.6  3 


The  center  of  gravity  of 
this  section  is  5.43  inches 
from  the  top  of  the  top  flange 
angles,  and  9.82  inches  from 
the  bottom  of  the  bottom 
flange  angles,  as  shown  in 
Fig.  22.  The  radius  of 
gyration  with  reference 
to  an  axis  at  right  angles 
fig.  22  to  the  webs  and  passing 

through  the  center  of  gravity  is  5.58  inches;  -  = 

r  5.58 


Center  of  Gravity 


v 


'•o 

<\i 


& 


J1 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  37 


=  38.7;  and  the  allowable  working  stress  (Table  XXXV) 
is  14,770  pounds  per  square  inch.  Then,  since  the  total 
stress  is  654,900  pounds,  the  required  area  of  cross-section 

is  =  44.34  square  inches.  As  the  section  tried  has 

14,770 

a  gross  area  greater  than  the  required  area,  it  will  be  used. 


46.  Location  of  Center  Line  of  Top  Chord. — The 
center  line  of  the  top  chord  will  be  placed  a  short  distance 
below  the  center  of  gravity  of  the  chord  section,  so  that  the 
bending  moment  due  to  the  eccentricity  of  the  stress  shall 
counteract  that  due  to  the  weight  of  the  member.  The 
eccentricity  will  be  calculated  for  the  heaviest  member  (D  E) . 
The  gross  area  of  D  E  is  44.63  square  inches,  and  the  weight 
of  this  member  per  foot  is  151.7  pounds.  To  provide  for 
latticing,  the  weight  will  be  taken  as  160  pounds  per  linear 
foot.  Then,  proceeding  as  in  Art.  41, 

'  =  8^654,900  X  12  =  * mch,  practically 

For  convenience,  it  is  well  to  have  the  center  line  the  same 
distance  from  the  back  of  the  angles  for  each  member,  so 
that  the  average  location  of  the  center  of  gravity  of  B  C,  CD, 

and  D  E  will  be  found.  It  is  _5. 43  _  535  jncjies> 

O 

or  5|  inches,  below  the  top  of  the  angles;  then,  the  center 
line  is  5f  +  i  =  5i  inches  below  the  top  of  the  top  flange 
angles.  The  different  positions  of  the  center  of  gravity  of 
the  top  chord  members  create  an  objection  to  the  use  of 
unsymmetrical  sections. 

47.  End  Post. — In  Desig7i  of  a  Highway  Truss  Bridge , 
it  was  found  necessary  to  revise  the  design  of  the  end  post 
after  the  wind  stresses  on  it  had  been  computed;  so,  in  the 
present  case,  the  end  post  will  not  be  designed  before  the 
wind  stresses  have  been  found.  For  the  purpose  of  compu¬ 
ting  the  exposed  area  of  the  web  members,  the  width  of  the 
end  post  will  be  taken  equal  to  that  of  the  top  chord. 


135—20 


38  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


DESIGN  OF  LATERAL  SYSTEM 


WIND  STRESSES 

48.  Wind  Pressure. — The  force  to  be  resisted  by  the 
lateral  system  consists  of  the  wind  pressure  on  the  train  and 
that  on  the  trusses,  as  specified  in  B.  S.y  Art.  27.  The  wind 
pressure  on  the  train  is  given  as  300  pounds  per  linear  foot 
of  track;  that  on  the  trusses  depends  on  the  exposed  area  of 
the  members.  To  find  the  exposed  area,  the  length  of  each 
member,  center  to  center  of  joints,  will  be  multiplied  by  the 
width  as  seen  in  elevation;  the  latter  width  will  be  taken 
1  inch  greater  than  the  width  of  web,  channel,  or  angle  that 
forms  the  member.  On  this  basis,  the  exposed  area  of  the 
web  members  of  one  truss  is  548  square  feet;  of  the  top 
chord,  144  square  feet;  and  of  the  bottom  chord,  192  square 
feet.  The  exposed  height  of  the  floor  will  be  taken  as  the 
distance  from  the  top  of  the  rail  to  the  top  of  the  bottom 
chord,  since  the  portion  of  the  floor  system  lower  than  this 
is  sheltered  by  the  bottom  chord.  In  Fig.  10  (a),  it  can  be 
seen  that  the  exposed  height  of  the  floor  is  about  3  feet; 
then,  the  exposed  area  will  be  3  X  144  =  432  square  feet. 

49.  Upper  Lateral  Truss. — The  upper  lateral  truss 
will  be  designed  to  resist  the  wind  pressure  on  the  top  chord 
and  one-half  that  on  the  web  members.  The  exposed  area 
of  the  top  chord  is  144  square  feet,  and  one-half  that  of  the 

548 

web  members  is  — -  =  274  square  feet;  the  combined 

A 

exposed  area  is,  therefore,  418  square  feet.  In  B.  S.,  Art.  27, 
it  is  specified  that  the  wind  pressure  shall  be  taken  as  50 
pounds  per  square  foot  on  twice  the  exposed  area  of  one 
truss,  when,  as  in  this  case,  it  produces  greater  stresses  than 
any  other  specified  wind  loading.  Then,  the  total  pressure 


30 


§  70  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 

to  be  resisted  by  the  top  lateral  truss  is  2  X  418  X  50  =  41,800 
pounds.  As  the  top  chord  is  108  feet  long,  this  corresponds 

to  or  Poun(^s  Per  linear  foot;  and,  since  the  panels 

are  18  feet  in  length,  the  panel  load  is  387  X  18  =  6,970 
pounds. 


The  upper  lateral  truss,  with  the  wind  panel  loads,  is  shown 


loads;  the  latter  do  not  affect  the  stresses  in  the  truss,  but 
will  be  considered  later  in  connection  with  the  portal.  The 
stresses  in  the  members,  determined  in  the  usual  way,  are 
shown  in  Fig.  24. 

50.  Lower  Lateral  Truss. — The  lower  lateral  truss 
will  be  designed  to  resist  the  wind  pressure  on  the  train,  and 


that  on  the  floor,  bottom  chord,  and  one-half  the  web  mem¬ 
bers.  It  is  necessary  in  every  case  to  ascertain  which  of  the 
two  alternative,  loadings  given  in  B.S.,  Art.  27,  causes  the 
greater  stresses. 

The  wind  pressure  of  300  pounds  per  linear  foot  on  the  train 
and  30  pounds  per  square  foot  on  one  truss  and  the  floor 
will  first  be  considered.  The  panel  load  due  to  the  pressure 
on  the  train  is  300  X  18  =  5,400  pounds,  and  will  be  taken 


40 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


as  a  live  panel  load.  The  exposed  area  of  the  floor  is 
432  square  feet;  that  of  the  bottom  chord,  192  square 
feet,  and  that  of  one-half  the  web  members,  274  square  feet; 
the  total  exposed  area  is,  then,  898  square  feet,  the  pressure 
on  which,  at  30  pounds  per  square  foot,  is  30  X  898  =  26,940 
pounds.  Since  the  bottom  chord  is  144  feet  long,  this  pres¬ 
sure  corresponds  to  — — — Q,  or  187,. pounds  per  linear  foot; 

144 

and,  since  the  panels  are  18  feet  in  length,  the  panel  load  is 
187  X  18  =  3,370  pounds.  The  total  panel  load,  including 
the  wind  pressure  on  the  train,  is,  therefore,  5,400  +  3,370 
=  8,770  pounds. 

The  alternative  wind  pressure  of  50  pounds  per  square 
foot  on  the  exposed  area  of  the  floor  plus  twice  the 
exposed  area  of  one  truss  will  now  be  considered.  The 
exposed  area  of  the  bottom  chord  is  192  square  feet;  one- 
half  that  of  the  web  members,  274  square  feet;  and  that  of 
the  floor,  432  square  feet.  Then,  the  total  wind  pressure 
on  the  lower  lateral  truss  is  50  X  [2(192 -f  274)  +  432] 
=  68,200  pounds.  Since  the  bottom  chord  is  144  feet  long, 

this  pressure  corresponds  to  -,  or  473.6,  pounds  per 

144 


linear  foot,  and,  since  the  panels  are  18  feet  in  length,  the 


panel  load  is  18  X  473.6  =  8,525  pounds.  Since  this  panel 
load  is  less  than  that  found  in  the  preceding  paragraph,  the 
latter  will  be  used,  as  it  will  cause  greater  stresses  in  the 
members  of  the  lateral  system. 

The  lower  lateral  truss  and  wind  panel  loads  are  shown  in 
Fig.  25.  There  are  seven  full  panel  loads  of  3,370  pounds 
each,  dead  wind  pressure,  and  seven  panel  loads  of  5,400 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  41 


pounds  each,  live  wind  pressure.  In  finding  the  stresses  in 
the  members  of  the  lateral  truss,  the  live  panel  loads  are 
assumed  to  be  placed  so  as  to  cause  the  greatest  stresses  in 
the  members,  in  the  same  way  that  vertical  live  load  is  con¬ 


sidered  in  finding  the  stresses  in  vertical  trusses.  The 
stresses  caused  in  the  members  of  the  bottom  lateral  truss 
by  the  combined  dead  and  live  wind  loads  are  shown  in 
Fig.  26.  The  half  panel  loads  at  a  and  a'  have  not  been 
considered,  because  they  are 
transmitted  directly  to  the 
masonry  and  do  not  affect 
the  stresses. 

5 1 .  Transverse  Frames. 

The  depth  of  portal  and 
transverse  frames  depends  on 
the  amount  of  room  above  the 
overhead  clearance  line.  The 
distance  between  the  center 
lines  of  the  chords  is  26  feet 
6  inches;  the  bottom  of  the 
bottom  chord  is  7}  inches 
below  the  center  line,  and  the 
top  of  the  cover-plate  of  the  top 
chord  is  about  6  inches  above 
the  center  line.  The  vertical 
distance  from  the  bottom  of 
the  bottom  chord  to  the  top  of  the  top  chord  is,  therefore,  27  feet 
7f  inches,  as  shown  in  Fig.  27.  Consulting  Fig.  10  (a),  it 
will  be  seen  that  the  base  of  the  rail  is  3  feet  9f  inches  above 


Fig.  27 


42 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


the  bottom  of  the  bottom  chord.  The  overhead  clearance 
line  is  22  feet  above  the  base  of  the  rail  (B.  S.,  Art.  18)  and 
25  feet  9f  inches  above  the  bottom  of  the  bottom  chord. 
This  leaves  27  feet  7f  inches  —  25  feet  9f  inches  =  1  foot 
10i  inches  from  the  top  of  the  top  chord  to  the  overhead 
clearance  line.  This  will  be  taken  as  the  depth  of  the 
transverse  frame. 

Curved  brackets  will  be  placed  at  each  end  of  each  frame. 
They  will  be  made  to  extend  out  as  far  as  the  clearance 

diagram  (B.  S .,  Art.  18) 


will  allow;  in  the  present 
case,  4  feet  6  inches  from 
the  center  of  the  truss,, 
They  can  be  made  con¬ 
siderably  deeper  than  this, 
but  it  is  customary  to 
make  the  depth  but  little 
greater  than  the  width.  In 
this  case,  they  will  be  made 
to  extend  5  feet  below  the 
bottom  of  the  frame.  The 
general  type  of  frame  and 
bracket  is  shown  in  Fig.  27. 

52.  Portal. —  Fig.  28 
is  a  plan  of  the  portal, 
portal  brackets,  and  end 
posts.  The  same  general 
type  of  frame  and  bracket 
will  be  used  as  for  the 
transverse  frames,  except 
that,  as  the  portal  is  only  about  2  feet  deep,  a  plate-girder 
portal  will  be  used.  The  portal  brackets  will  extend  4.5  feet 
out  from  the  center  of  the  end  post;  the  other  dimensions 
shown  in  Fig.  28  are  found  from  the  corresponding  dimen¬ 
sions  in  Fig.  27,  by  multiplying  the  latter  by  esc  H  (1.209). 

The  force  P  that  acts  at  the  top  of  the  portal  is  one-half 
the  total  wind  pressure  on  the  upper  chord,  or  20,900 


Fig.  28 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  43 


pounds.  Making-  use  of  the  formulas  given  in  Stresses  in 
Bridge  Trusses,  Part  5,  assuming  the  point  of  inflection  of 
the  end  post  to  be  half  way  between  the  bottom  of  the 
bracket  and  the  bottom  of  the  post,  the  stresses  are  found 
to  be  practically  as  follows: 

Direct  stress  in  end  posts, 

—  =  20,900  X  20.84  =  27  200  pounds 
b  16 


Bending  moment  on  end  posts, 


P 


(hf  —  d  —  d')  =  10,450  X  12.58  X  12  =  1,577,500  inch-pounds 
Shear  on  portal, 

—  =  20’900  *  20,84  =  27,200  pounds 
b  16 

In  the  plate-girder  portal,  the  flanges  are  assumed  to 
resist  the  entire  bending  moment,  and  the  required  area  at 


any  section  is  found  by  means  of  the  formula  A  = 


M 


s  h 


in 


•g 


which  M  is  the  moment  about  a  point  in  the  opposite 
flange  directly  opposite  the  section  under  consideration. 
The  formula  for  moments  about  points  in  the  top  flange  is 

jyr  _  P  h'  _P  Jl'  X 
~  ~2 

At  F,  x  =  4.5,  and  at  F' ,  x  =  11.5;  then, 

20,900  X  20.84  20,900  X  20.84  X  4.5 


moment  at  F  = 


moment  at  F'  = 


2  16 
=  95,300  foot-pounds; 

20,900  X  20.84  20,900  X  20.84  X  11.5 


2  16 
=  —  95,300  foot-pounds 

The  formula  for  moments  about  points  in  the  bottom 
flange  is 

M=  Ph!  Pd  Ph'x 

2  '  2  b 

At  D,  x  —  4.5,  and  at  D' ,  x  =  11.5;  then, 


moment  at  D  = 


20,900  X  20.84  .  20,900  X  2.22 
2  *  2 

_  20,900  X  20.84  X  =  118  500  foot-pounds; 


16 


44 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


.  f  n/  20,900  X  20.84  .  20,900  X  2.22 
moment  at  D'  —  — - - - — — - 

2  2 


20,900  X  20.84  X  11.5 
16 


=  72,100  foot-pounds 


The  value  of  hs  is  not  known,  but  may  be  assumed  as  a 
little  less  than  d;  in  this  case,  it  will  be  assumed  as  equal  to 
24  inches.  Since  the  above  moments  are  of  one  kind  when 
the  wind  blows  in  the  direction  shown,  and  of  the  other 
kind  when  it  blows  in  the  opposite  direction,  the  stresses  in 
the  flanges  reverse,  and  in  finding  the  required  area  of 
flange,  the  greatest  moment  in  each  flange  must  be  increased 
by  .8  of  the  moment  at  the  other  point  in  the  same  flange 
( B .  S.,  Art.  34).  The  greatest  moment  in  the  lower- 
flange  is  at  D.  Then,  the  required  area  of  the  upper  flange 
is  (118,50°  +  .8  X  72, 100)j2  =  6.51  square  inche,  The 
16,000  X  24 

moments  at  th.e  two  ends  of  the  upper  flange  are  the  same. 

Then,  the  required  area  of  the  lower  flange  is 

l.f  X  95,300  X  12  K  da  •  i 

—  - - — r -  =  5.36  square  inches 

j.6,000  X  24 

There  is  also  a  direct  stress  caused  in  the  bottom  chords 
of  the  trusses  by  the  direct  stress  in  the  end  post;  it  is 

P  h' 

found  bv  multiplying - by  cos  H ,  which  gives  27,200 

b 

X  .5619  =  15,300  pounds,  compression  on  the  windward,  and 
tension  on  the  leeward,  side;  only  the  latter  stress  need  be 
considered,  since  the  former  simply  decreases  the  tension  in 
the  bottom  chord. 


DESIGN  OF  MEMBERS 

53.  Upper  Lateral  Truss.- — Comparing  the  wind 
stresses  in  the  top  chord  members  as  given  in  Fig.  24  with 
the  combined  dead-  and  live-load  stresses  as  given  in  Fig.  14, 
it  is  seen  that  the  former  are  in  no  case  as  great  as  25  per 
cent,  of  the  latter,  so  that  they  need  not  be  considered. 

For  the  diagonals,  it  is  well  first  to  find  the  allowable 
stress  in  the  smallest  member  that  can  be  used.  In  B.  S.} 
Art.  86,  it  is  specified  that  no  member  of  a  lateral  truss 


§  79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


45 


shall  be  less  than  Si  in.  X  Si  in.  X  t  in.  Allowing  for  one 
i-inch  rivet  hole,  the  net  area  of  one  angle  of  these  dimensions 
is  found  to  be  2.48  —  .38  =  2.10  square  inches.  Since  the 
working  stress  in  tension  is  16,000  pounds  per  square  inch, 
the  allowable  stress  in  one  angle  is  2.1  X  16,000  =  33,600 
pounds.  As  this  is  greater  than  the  stress  in  any  diagonal 
of  the  upper  lateral  truss,  one  Si"  X  Si"  X  i"  angle  will  be 
used  for  each  member. 

The  transverse  strut  will  be  made  as  shown  in  Fig.  29, 
which  is  a  customary  form.  Each  flange  will  be  composed 
of  two  Si"  X  Si"  X  i"  angles  connected  by  double  latticing 
of  S"  X  t"  bars.  In  the  present  case,  as  the  greatest  stress 


Fig.  29 


in  a  transverse  strut  is  17,400  pounds  (member  C Clf  Fig.  24), 
these  angles  are  sufficiently  large. 

54.  Lower  Lateral  Truss.- — In  the'design  of  the  upper 
lateral  truss,  it  was  found  that  the  allowable  stress  in  one 
Si"  X  Si"  X  a"  angle  is  33,600  pounds.  As  this  is  greater 
than  the  stresses  in  the  diagonals  in  the  panels  cd  and  de. 
Fig.  26,  one  Si"  X  Si"  X  i"  angle  will  be  used  for  each  of 
the  diagonals  in  these  panels. 

In  the  panel  be ,  the  required  net  area  of  each  diagonal  is 

=  2.13  square  inches.  One  Si"  X  Si"  X  tV'  angle 

will  be  used. (net  area  =  2.87  —  .44  =  2.43  square  inches). 
In  the  panel  a  bf  the  required  net  area  of  each  diagonal  is 

LTTTr!?!  =  2*89  square  inches.  One  Si"  X  Si"  X  tV'  angle 
16,000 

will  be  used  (net  area  =  3.62  —  .56  —  3.06  square  inches). 


46  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


The  wind  stresses  in  the  lower  chord  members  are  less 
than  25  per  cent,  of  the  combined  dead-  and  live-load  stresses, 
and  so  need  not  be  considered. 


55.  Portal. — The  shear  on  the  portal  was  found  in 
Art.  52  to  be  27,200  pounds.  This  is  treated  in  exactly  the 
same  way  as  the  shear  on  any  other  plate  girder.  A  web 
I  inch  thick  will  be  used;  the  depth  2.22  feet  will,  for 
convenience,  be  called  26  inches.  Then,  the  intensity  of 

shearing  stress  is  ^,200  =  2,790  pounds  per  square  inch. 

26  X  t 

Consulting  Table  XXXVI,  it  is  seen  that  the  allowable 
unsupported  distance  is  37  inches;  so  that  no  stiffeners  are 
required. 

The  required  net  area  of  the  top  flange  is  5.51  square 
inches,  and  that  of  the  lower  flange  is  5.36  square  inches 
(Art.  52).  It  is  customary  to  make  the  section  of  the  top 
and  bottom  flanges  the  same.  Two  b"  X  3"  X  iV7  angles  will 
be  used  for  each  [net  area  =  2(3.31  —  .44)  —  5.74  square 
inches] . 

The  required  pitch  of  flange  rivets,  computed  by  the 
formula  used  in  Art.  13,  comes  out  greater  than  6  inches, 
so  that  a  pitch  of  6  inches  will  be  used  ( B .  S.,  Art.  41). 


56.  Design  of  End  Post. — The  combined  dead-  and 
live-load  stress  in  the  end  post  is  shown  in  Fig.  14  to  be 
527,800  pounds.  The  direct  stress  due  to  the  wind  is 
27,200  pounds;  the  total  stress  is,  therefore, 

527,800  +  27,200  =  555,000  pounds 
In  addition,  there  is  a  bending  moment  due  to  the  wind 
equal  to  1,577,500  inch-pounds  (Art.  52).  The  following 
section  will  be  used: 

Gross  Area, 
in  Square  Inches 


1  cover-plate  22  in.  X  f  in.  1  3.7  5 

2  top  flange  angles  3|-  in.  X  3i  in.  X  f  in.  7.9  6 

2  web-plates  15  in.  X  I  in.  1  5.00 

2  side  plates  8  in.  X  i  in.  1  0.00 

2  bottom  flange  angles  3i  in.  X  3i  in.  X  i  in.  7.9  6 

Total  gross  area  =  5  4.67 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  47 


These  shapes  will  be  placed  as  shown  in  Fig.  30,  the  edge 
of  the  top  flange  angles  being  made  flush  with  the  edge  of 
the  cover-plate.  Consulting  Table  XI,  and  applying  the  rule 
given  in  Bridge  Members  and  .Details,  the  actual  width  of  the 
leg  of  a  3J"  X  3-i"  X  i"  angle  is  found  to  be  3f  inches.  Since 
the  width  of  the  cover-plate  is  22  inches,  the  distance  between 
the  vertical  legs  of  the  flange  angles  is  22  —  3i  —  3f  =  14| 
inches;  since  the  webs  are  i  inch  thick,  the  clear  distance 
between  them  is  13f  inches.  The  length  of  the  end  post 
center  to  center  of  connections  is  32.035  feet  =  384.4  inches; 
the  radius  of  gyration  with  respect  to  the  axis  X'  X  pass¬ 
ing  through  the  center  of  gravity  of  the  section,  which  is 
5.63  inches  from  the  top  of  the  top  flange  angles,  and  9.62 
inches  from  the  bottom 
of  the  bottom  flange 
angles,  is  5.55  inches. 


Then,  —  = 
r 


384.4 


=  69.3, 


J 

x*  \ 

Cenfer  of 

Gravity 

ITT 

„ _  /S3"- 

I  ^ 

k  |  Ik 

aj  T 
0\  1 

J 

. 

w  >  j 

5.55 

and  the  working  stress 
(Table  XXXV)  is  12,630 
pounds  per  square  inch. 

The  working  stress  for 
the  combined  dead,  live, 
and  wind  stresses  will 
be  taken  25  per  cent, 
greater  than  this,  or  1.25  X  12,630  =  15,790  pounds  per  square 
inch,  as  explained  in  Design  of  a  Highway  Truss  Bridge. 

Since  the  total  combined  direct  stress  is  555,000  pounds,  and 
the  area  of  cross-section  is  54.67  square  inches,  the  intensity  of 


r 

Fig 


9  f 


30 


direct  stress  is 


555,000 


=  10,150  pounds  per  square  inch.  The 


54.67 

intensity  of  stress  due  to  bending  will  be  found  from  the  formula 

Me 


s  — 


I 


in  which  M  =  bending  moment; 

c  =  distance  to  the  extreme  fiber; 

/  =  moment  of  inertia  of  the  section  about  the 
axis  Yf  Y,  Fig.  30. 


48 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  71) 


The  value  of  /  is  found  to  be  3,068.  Then, 

s  =  1*577,500  X  11  _  f^00q  pOUnds  per  square  inch 
3,068 

Then,  the  total  fiber  stress  is  10,150  -f-  5,660  =  15,810 
pounds  per  square  inch.  This  is  greater  than  the  allow¬ 
able  intensity  of  stress,  but,  as  the  difference  is  very  little, 
there  is  no  necessity  of  revising  the  section. 


DETAILS 


CHORD  SPLICES 

57.  Splice  in  Top  Chord. — The  top  chord  will  be  spliced 
in  panel  CD,  Fig.  14,  just  to  the  left  of  D.  The  splice  will 
be  composed  of  the  following  shapes,  the  total  gross  area 
of  which  is  slightly  less  than  the  gross  area  of  CD,  but  is 
sufficient: 

Gross  Area, 
in  Square  Inches 


1  cover-plate  22  in.  X  2  in. 

11.00 

2  inside  web-plates  15  in.  X  "re  in. 

13.125 

2  outside  side  plates  14  in.  X  2  in. 

14.0  0 

2  bottom  flange  plates  3i  in.  X  t  in. 

2.625 

Total  area 

=  40.750 

Each  part  should  have  sufficient  rivets  on  each  side  of  the 
splice  to  transmit  its  proportion  of  the  total  stress.  The  pro¬ 
portion  transmitted  by  each  portion  is  found  by  multiplying 
its  gross  area  by  the  working  stress  for  the  member  CD 
(14,740  pounds  per  square  inch,  Art.  45).  The  number  of 
rivets  is  found  by  dividing  this  stress  by  the  value  of  one 
rivet;  l-inch  rivets  are  used,  shop  driven  on  one  side  of  the 
splice,  and  field  driven  on  the  other  side.  The  value  of  a 
field  rivet  in  single  shear,  5,410  pounds,  will  be  used  and  the 
same  number  of  rivets  put  in  on  each  side  of  the  joint.  The 
required  number  of  rivets  in  each  of  the  different  splice 
plates  is  as  follows: 

i  r  w  oo-  v/i-  11.00  X  14,740  onr>  . 

1  splice  plate  22  m.X  2  in., - -J - =  30.0  rivets 

5,410 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  49 


i  r  ,  ,  1  r  •  w  7  .  6.56  x  14,740  1^7  0  in  •  , 

1  web-plate  15  in.  X  ie  in., - -P7-7-2 - =  17.9,  say  18,  rivets 

5,410 

i  •  j  i  4,  i  a  ‘  w  i  •  7.00  X  14,740  io  i  o n  ■ 

1  side  plate  14  in.  X  £  in., - - =  19.1,  say  20,  rivets 

5,410 

1  bottom  plate  3^  in.  X  f  in.,^^ J*  —  =  3.6,  say  4,  rivets 

5,410 

The  splice  is  shown  in  Fig.  31,  in  which  (a)  is  the  top  view, 


Q  O  O  ON 

L  O 

>" 


•  iQ  Q  Q  Q 


O 

Q 

JQ 

• 

• 

•  •  • 

•  •  •  • 

•  •  • 

O  Q  Q  jO 
O  O  O  Oj 

O  O  O  )Oi 

O^ 

O 

O 

O  \ 

•  •  • 

O  O  O  O'/  O 

2  P/crfeTJpAf? 


f  Plate  /4"Ai 


(b)  the  elevation,  and  ( c )  the  section  and  bottom  view.  The 
correct  number  of  rivets  is  shown  in  each  splice  plate;  it  is 
customary  to  space  the  rivets  in  splices  from  2  to  3  inches 
apart  when  staggered,  as  shown;  in  the  figure,  thfe  pitch  is 


50  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


about  2a  inches  The  latticing  is  continued  right  along  by 
the  splice,  in  the  same  way  as  for  the  rest  of  the  member. 

58.  Splice  in  Bottom  Cliord. — The  bottom  chord  will 
be  spliced  in  panel  cd  (Fig.  14)  just  to  the  left  of  d.  The 
method  of  splicing  is  precisely  the  same  as  for  the  top  chord, 


/ 

/ 

/ 

•  •  •  •  |0  O  0  0 

\ 

\  i 

- ^ -  ! 

0  j  • 

•  •  •  ~l  0  0  0 

01  of 

0! 

•  •  •  *10000 

10 

0  ;• 

•  •  •  |  0  0  0 

0]  0 

\ 

\ 

\ 

•  •  •  *10000 

/ 

/ 

(b) 


except  that  in  this  case  net  area  must  be  considered  instead 

of  gross  area.  The  following  splice  plates  will  be  used: 

Net  Area, 
in  Square  Inches 

4  plates  4  in.  X  i^6  in.,  4(2.25  —  .56)  =  6.7  6 

2  inside  plates  15  in.  X  us  in.,  2(8.44  —  3  X  .56)  =  1  3.5  2 

2  outside  plates  14  in.  X  iin.,  2(7  —  3  X  .50)  =  1  1.0  0 

Total  area  =  3  1.2  8 


i 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


51 


The  number  of  rivets  required  to  connect  each  of  the  splice 

plates  on  each  side  of  the  joint  is  as  follows: 

h  i  ,  A  .  9  •  1.69  X  16,000  c  a  •  + 

1  plate  4  in.  X  Te  in., - „  -  =  5.0  rivets 

5,410 

i  .  i  c  •  w  9  •  6.76  X  16,000  on  . 

1  plate  15  in.  X  Te  m., - -  -  =  20  rivets 

5,410 

1  plate  14  in.  X  2  in., - - - - -  =  16.3  rivets 

5,410 

The  splice  is  shown  in  Fig.  32,  in  which  (a)  is  the  top 
view,  ( b )  the  elevation,  and  ( c )  a  section  and  bottom  view. 
The  required  number  of  rivets  is  shown  in  each  splice  plate. 


TRUSS  JOINTS 


59.  The  general  method  of  connecting  the  members  of 
riveted  trusses  to  each  other  by  means  of  connection  plates 
or  gussets  has  been  explained  in  Bridge  Members  a?id  Details . 
The  connection  of  the  members  to  each  other  at  the  differ¬ 
ent  joints  of  the  truss  under  consideration  will  now  be  dis¬ 
cussed.  The  rivets  that  connect  the  members  to  the  gussets 
are  i  inch  in  diameter,  and  are  part  shop  driven  and  part  field 
driven.  The  value  of  each  rivet  in  single  shear  is  the  small¬ 
est  and  the  only  one  that  need  be  considered.  As  most  of 
the  rivets  are  field  driven,  the  value  for  field-driven  rivets, 
which  is  5,410  pounds,  will  be  used,  and  the  number  of  rivets 
required  to  transmit  the  stress  to  and  from  each  member  will 
be  first  calculated.  These  numbers  are  as  follows: 

Member  Number  of  Rivets 


BC 
a  B 
Be 
Cd 

De 


496.600 
5,410 

527,800 

5,410 

400,400 

5,410 

281.600 
5,410 

174,600 

5,410 


=  92,  or  46  on  each  side 
—  98,  or  49  on  each  side 
=  74,  or  37  on  each  side 
=  52,  or  26  on  each  side 
=  33,  or  17  on  each  side 


52  '  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


Member 

dE 

a  b 

Bb 

Cc 

Dd 

Ee 


Number  of  Rivets 


84.900 

5,410 
296,600 

5,410 

162,300 

5,410 

239.900 

5,410 

151,400 

5,410 

77,200 

5,410 


16,  or  8  on  each  side 
55,  or  28  on  each  side 
30,  or  15  on  each  side 
45,  or  23  on  each  side 
28,  or  14  on  each  side 
14,  or  7  on  each  side 


As  c  D  was  made  larger  than  necessary,  to  conform  to  the 
rule  that  no  counter  shall  have  an  area  less  than  3  square 
inches,  the  number  of  rivets  will  be  found  for  the  stress  that 
the  section  chosen  can  transmit  at  16,000  pounds  per  square 
inch.  Since  the  net  area  of  c D  is  3.47  square  inches  (Art. 
42),  the  required  number  of  rivets  is 


3.47  X  16,000  =  1Q  3  6  h  ;d 

5,410 

60.  Joint  B. — Fig.  33  shows  joint  B :  (a)  is  the  eleva¬ 
tion  of  the  joint,  and  shows  one  of  the  gussets  e  that  are 
riveted  to  the  inside  of  the  top  chord  and  end  post,  and  to 
the  ends  of  the  members  aB,  B  b,  Be ,  and  B  C  that  meet  at 
the  joint;  ( b )  is  the  elevation  of  the  end  of  the  portal^  and 
portal  bracket  h  where  they  connect  to  the  end  post;  (e)  is 
the  top  view  of  the  end  of  the  top  angles  of  the  portal,  and 
shows  the  bent  plate  i  that  connects  the  angles  to  the  top 
chord  of  the  truss;  (d)  is  the  plan  of  the  top  chord,  and 
shows  in  section  at  the  lower  right-hand  side  a  portion  of 
the  bottom  flange  of  the  top  chord.  The  lines  aB ,  B  b,  Be , 
and  B  C  are  the  center  lines  of  the  different  members,  and 
meet  at  the  point  B\  the  end  post  and  top  chord  are  cut  off 
on  the  line  //  that  bisects  the  angle  between  them. 

In  drawing  a  riveted  joint,  the  center  lines  of  the  members 
are  first  drawn,  and  then  the  lines  that  represent  the  members 


I 


79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  53 


themselves  are  drawn  parallel  to  the  center  lines.  The 
gauge  lines  of  the  rivets  are  next  drawn,  and  the  rivets  are 
spaced  on  these  lines  according  to  the  rules  for  rivet  spacing. 
In  locating  the  gauge  lines  of  angles,  the  distances  to  be  used 
are  the  standard  distances  given  in  Table  XII;  in  locating 
gauge  lines  on  plates,  two  lines  are  first  drawn  parallel  to 
the  edges  of  the  plate  and  I2  or  If  inches  from  them, 
as  /,/  in  the  end  post.  If  they  are  more  than  about  4i  inches 
apart,  one  or  more  lines  from  2}  to  4  inches  apart  are  drawn 
between  them,  as  in  the  case  of  the  top  chord.  The  rivets 
are  located  on  these  lines  and  staggered  in  such  manner  that 
they  will  be  not  nearer  to  each  other  than  3  inches;  they  are 
in  general  spaced  closer  in  compression  members  than  in 
tension  members. 

The  pitch  of  rivets  in  the  end  post,  Fig.  33  ( a ),  is  about 
l!  inches;  in  the  top  chord,  2f  inches;  and  in  the  main 
diagonal,  about  2\  inches.  When  convenient,  lug  angles  / 
are  riveted  to  the  outstanding  legs  of  the  angles  of  the 
main  members,  so  as  to  spread  or  distribute  the  stress  over 
a  greater  width  of  gusset.  Plates  i  inch  thick  will  be  used 
for  the  gussets  e ,  as  they  are  found  to  furnish  sufficient 
section.  One-half  of  B  c  is  placed  outside  of  the  gusset  on 
each  side;  the  two  halves  are  connected  below  the  gusset  by 
tie-plates  771  and  lattice  bars.  The  two  channels  that  com¬ 
pose  the  vertical  Bb  are  inserted  between  the  gussets  and 
connected  to  each  other  below  them  by  tie-plates  n  and 
latticing.  There  are  more  rivets  than  necessary  in  this 
member,  on  account  of  the  fact  that  the  rivets  in  the  end 
post  and  main  diagonal  control  the  size  of  the  gusset,  and 
the  rivets  in  the  vertical  are  spaced  about  3i  inches  apart  to 
hold  the  gussets  and  channels  together  more  tightly.  The 
rivets  in  the  upper  end  of  the  vertical  are  also  counted  with 
the  end  post  and  top  chord.  Some  designers  prefer  not  to 
count  a  rivet  twice;  but  when,  as  in  this  case,  the  members 
are  on  opposite  sides  of  the  gusset,  there  is  no  reason  why 
they  should  not  be  counted;  in  such  a  case,  however,  allow¬ 
ance  should  be  made  by  providing  more  rivets  than  are 
required  by  the  computation. 

135—21 


54  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


In  order  to  save  extra  work  in  handling  and  riveting,  the 
gussets  are  usually  riveted  in  the  shop  to  one  of  the  members. 
In  Fig.  33,  they  are  shown  riveted  to  the  top  chord;  on  this 
account  less  rivets  are  required,  since  the  value  of  a  shop- 
driven  rivet  is  greater  than  that  of  a  field-driven  rivet. 

61.  The  cross-section  of  the  portal  is  shown  at  oo , 
Fig.  33  ( a ).  The  lowest  point  p  of  the  lower  flange  of  the 
portal  is  made  level  with  the  bottom  of  the  transverse  struts 
of  the  intermediate  panel  points.  The  top  flange  angles  are 
placed  high  enough  to  continue  right  across  the  top  chord, 
as  shown  at  g,  and  are  connected  to  it  by  means  of  the  bent 
plates  i  and  r.  The  web  of  the  portal  is  spliced  at  ss, 
Fig.  33  (b) ,  and  the  portion  toward  the  truss  is  continued 
down  to  form  the  web  of  the  bracket.  This  portion  is  con¬ 
nected  to  the  end  post  by  means  of  the  connection  angles  t, 
which  are  usually  3fin.  X  3iin.  X  fin.  The  rivets  in  these 
connection  angles  are  spaced  about  6  inches  apart,  except  at 
the  upper  end,  where  those  which  also  transmit  the  stress 
from  the  gusset  to  the  end  post  are  spaced  3  inches  apart. 

The  diagonal  in  the  end  panel  of  the  top  lateral  truss  is 
connected  to  the  bent  plate  i,  as  shown  at  u  in  Fig.  33  ( d ), 
a  lug  angle  being  riveted  to  the  main  angle. 

62.  Joint  C. — Fig.  34  shows  the  connection  at  joint  C: 
(a)  is  the  elevation  of  the  joint,  showing  one  of  the  gussets  d 
and  portions  of  the  members  B  C,  CD,  Cc,  and  Cd ;  it  also  shows 
a  cross-section  h  h  of  the  strut  and  the  connection  of  the  strut 
to  the  vertical;  (b)  is  an  elevation  of  an  intermediate  cross¬ 
strut  and  bracket;  (c)  is  a  top  view  of  the  top  chord,  and 
shows  the  connection  of  the  diagonals  z,  i  of  the  upper  lateral 
truss  to  the  chord  by  means  of  the  plate  /.  At  the  top  of  the 
vertical,  which  lies  between  the  gussets,  a  diaphragm^  is  riv¬ 
eted  between  the  channels,  in  order  to  distribute  the  stress 
between  the  sides  of  the  truss.  The  same  remarks  with 
regard  to  spacing  of  rivets,  etc.  apply  here  as  in  the  case  of 
joint  B.  There  is  a  small  excess  of  rivets  in  the  vertical, 
but  this  is  a  frequent  occurrence,  and  is  done  to  get  even  spa¬ 
cing  in  the  gussets.  In  the  remaining  top  chord  joints,  the 


, 

. 


' 


' 1 


i. 


--ass-  ■ 


■ 


135  §  79 


•'iQ.  34 


' 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  55 


cross-strut  and  bracket  connection  will  not  be  shown,  but  the 
holes  for  the  connection  of  the  strut  to  the  vertical  will  be 


D 


shown.  In  Fig.  34  (c) ,  a  short  portion  of  the  top  chord  at 
the  lower  right-hand  side  is  given  in  section,  so  as  to  show 
the  tie-plate  j  and  part  of  the  lattice  bar  k. 


E 


e  • 

Pig.  36 

63.  Joints  Z)  and  E. — Figs.  35  and  36  represent  the 
joints  at  D  and  Et  respectively.  The  connection  of  the 


56  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


laterals  and  of  the  transverse  frame  and  bracket  is  the  same 
here  as  at  joint  C.  In  Fig.  35,  the  counter  c  D  at  the  left  is 
placed  inside  the  gussets,  so  as  to  clear  the  main  diagonal  Cd 
where  they  cross  each  other  at  the  center  of  the  panel.  For 
the  same  reason,  counter  dE,  Fig.  36,  is  placed  inside  the 
gusset  so  it  will  not  interfere  with  the  main  diagonal  D  e.  The 
counters  consist  of  two  angles  each,  one  on  each  side,  and  it  is 
customary  to  place  the  angles  so  that  the  center  of  gravity 
shall  coincide  with  the  center  line  of  the  member.  This  is 
frequently  done  in  the  case  of  laterals  that  consist  of  single 
angles;  but  in  the  latter  case  it  is  customary  to  connect  them 
as  shown  in  Fig.  34  (<:),  making  the  back  of  the  angle  coincide 
with  the  center  line.  *  Diaphragms  are  placed  inside  the  ver¬ 
ticals  D  d  and  Ee  at  the  ends,  and  the  same  spacing  of  rivets 
is  used  as  for  Cc,  so  that  the  connection  of  the  transverse 
struts  will  all  be  the  same. 

64.  Joint  a. — Fig.  37  represents  the  joint  a.  In  this 
figure,  ( a )  is  the  elevation,  and  shows  one  of  the  gussets  b 
that  connect  the  end  post  and  the  bottom  chord,  both  these 
members  being  placed  outside  the  gussets.  The  center  lines 
and  gauge  lines  are  first  laid  off,  and  then  the  rivets  are 
spaced  along  these  lines.  Those  in  the  end  post  are  spaced 
about  2i  inches  apart  and  staggered  as  shown,  until  a  suffi¬ 
cient  number  of  rivets  is  obtained,  when  the  gusset  is  cut  off 
square  with  the  end  post,  as  shown  at  c.  The  right-hand 
edge  of  the  gusset  is  then  carried  vertically  downwards  into 
the  bottom  chord,  as  shown  at  d ,  and  rivets  are  spaced  about 
3  inches  apart  from  d  to  the  end  of  this  member.  It  is  sel¬ 
dom  necessary  to  count  the  numbers  of  rivets  in  the  bottom 
chord  connection,  for  the  above  spacing  invariably  gives 
sufficient  rivets.  Stiffeners  e  are  placed  both  outside  and 
inside  of  the  connection  over  the  pedestal  to  transmit  the 
load  to  the  bearing.  The  stiffener/,  together  with  <?',  serves 
for  the  connection  of  the  end  frame,  as  shown  at  (d).  The 
other  end  of  this  frame  connects  to  the  end  stringer.  At 
the  center  of  the  shoe,  a  diaphragm^,  shown  at  (a)  and  (c), 
consisting  of  a  web  and  four  angles,  is  riveted  to  the  inside 


135  §79 


I 

I 


I 

I 


I 

I 


Center  Line  o/-  Truss 


I 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  57 

of  the  gussets.  A  sole  plate  h  about  1  inch  in  thick¬ 
ness  is  riveted  to  the  outstanding  legs  of  the  bottom  flange 
angles. 

Practice  differs  considerably  as  to  the  method  of  finding  the 
end  of  the  bottom  chord  and  the  gusset.  The  length  of  truss 
beyond  the  point  a  depends  on  the  required  size  of  shoe,  the 
bottom  chord  being  carried  out  to  the  end  of  the  shoe  and 
cut  off  square,  as  shown  at  z.  Some  designers  continue  the 
cover-plate  of  the  end  post  straight  down  to  its  intersection 
with  the  top  flange  of  the  bottom  chord,  and  continue  the 
edge  of  the  gusset  along  that  line,  as  shown  by  the  dotted 
line//.  The  load,  however,  is  distributed  over  the  bearing 


much  more  evenly  if  the  gusset  is  carried  up  to -the  top  of 
the  bottom  chord  at  its  end  and  then  straight  up  on  the 
line  k  k'  to  the  top  of  the  gusset.  This  makes  it  necessary 
to  splice  the  top  cover-plate  of  the  end  post  at  k'\  a  plate  of  the 
same  thickness  as  the  cover-plate  is  fastened  to  the  edge  of 
the  gusset  by  means  of  the  angles  l  and  and  is  spliced  to 
the  cover-plate  by  means  of  the  bent  splice  plate  m.  The 
right-hand  edge  of  the  gusset  is  stiffened  by  3"  X  3"  X  t" 
angles,  as  shown  at  n. 


58  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


Fig.  37  ( b )  is  a  plan  of  the  end  post;  the  upper  left-hand 
half  is  a  top  view  of  the  cover-plate,  and  the  lower  right-hand 
half  is  a  section  through  the  gusset,  and  a  plan  of  the  bottom 
flange  of  the  end  post.  The  pedestal  and  rollers  will  be 
discussed  later. 

65.  Joint  b. — Fig.  38  shows  joint  b.  No  stress  is  trans¬ 
mitted  from  one  member  to  another  at  this  joint,  except  the 
load  from  the  floorbeam  to  the  vertical,  so  that  no  gusset  is 


required  to  connect  the  vertical  and  the  chord.  It  is  cus¬ 
tomary,  however,  to  provide  a  small  gusset  d ,  a  little  wider 
on  each  side  than  the  vertical,  in  order  to  fill  up  the  space 
between  the  vertical  and  the  chord,  and  to  make  the  joint  a 
little  stiffen  The  plate  e  is  for  the  purpose  of  filling  up  the 
space  between  the  flange  angles  of  the  bottom  chord. 

66.  Joints  c,  d,  and  e . — Figs.  39,  40,  and  41  show,  respect¬ 
ively,  joints  c ,  d,  and  e.  These  joints  are  somewhat  simpler 


50 


§  79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE 


e 


Fig.  41 


GO 


DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §  79 


than  joint  a ,  but  the  same  general  rules  are  observed  in 
laying  them  out.  The  only  point  in  connection  with  these 
joints  that  requires  special  attention  is  the  connection  of  the 
verticals  to  the  gussets.  It  should  be  remembered  that  the 
rivets  in  the  two  rows  a,  a  near  the  center  of  the  vertical  trans¬ 
mit  the  load  from  the  floorbeam  to  the  truss,  and  should  not 
be  counted  as  transmitting  any  stress  from  the  vertical  to 
the  gusset;  there  should  be  sufficient  rivets  in  the  lines  b,  b 
outside  of  these  two  lines  to  transmit  this  stress.  When,  as 
in  the  case  of  Cc ,  Fig.  39,  the  channel  is  15  inches  in  width, 
additional  rows  can  be  driven  through  the  web  of  the  channel 
on  each  side  of  the  floorbeam  connection  angles.  When,  as 
in  the  case  of  D  d.  Fig.  40,  and  Ee ,  Fig.  41,  the  channel  is 


Fig.  42 


not  wide  enough  to  allow  extra  rows  to  be  driven,  lug  angles  / 
are  riveted  to  the  flanges  of  the  channels,  and  the  required 
number  of  rivets  is  driven  in  the  legs  of  these  lug  angles 
that  are  in  contact  with  the  gussets. 

67.  Bottom  ^Lateral  Connection. — Fig.  42  shows  a 
connection  of  the  lower  laterals  a ,  a  to  the  lateral  connection 
plate  k  shown  in  Fig.  10,  and  the  connection  of  the  latter  to 
the  truss.  The  vertical  b  b  and  the  diaphragm  c  are  shown 
in  cross-section,  as  well  as  the  sides  d ,  d  of  the  bottom 
chord,  and  the  gussets  e,  e.  The  figure  also  shows  the  tie- 
plate  //  and  lattice  bars  on  the  bottom  of  the  bottom  chord. 
The  connections  at  the  joints  a,b,c,  and  d ,  Fig.  25,  are 


§79  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  61 


similar  to  this  connection,  except  that,  where  necessary, 
more  rivets  are  driven  and  the  lateral  plate  is  made  some¬ 
what  larger.  The  rivets  in  the  lateral  and  lug  angles  are 
a  inch  in  diameter.  Both  diagonals  in  each  panel  are  placed 
on  top  of  the  connection  plate,  in  order  that  they  may  be  in 
better  position  to  connect  to 
the  stringers  where  they  inter¬ 
sect  them. 

The  method  of  crossing  the 
laterals  at  the  center  of  the  panel 
is  shown  in  Fig.  43:  one  diag¬ 
onal  a  continues  unbroken,  and 
the  other  b  b  leads  up  to  it  on 
each  side,  and  is  spliced  by  a 
plate  cc ,  which  is  also  riveted 
to  the  angle  a. 

The  connection  to  the  bottom  flange  of  the  stringer  is 
shown  in  Fig.  44:  the  lug  angle  k  connects  the  lateral 
angle  l  with  the  bottom  flange  of  the  stringer  m. 


BEARINGS 

68.  Required  Area. 
The  required  area  of  bear¬ 
ing  for  each  end  of  each 
truss  is  found  by  dividing 
the  reaction  by  the  allow¬ 
able  or  working  pressure 
on  the  masonry.  As  there 
is  no  end  floorbeam,  the 
reaction  is  equal  to  the 
vertical  component  of  the  stress  in  the  end  post,  that  is,  436,600 
pounds  (Art.  37).  The  allowable  pressure  on  the  masonry 
is  given  in  B.  S .,  Art.  29,  as  500  pounds  per  square  inch. 

Then,  the  required  area  is  =  873  square  inches.  If 

the  bed-plate  is  square,  it  must  be  about  30  inches  on  each 
side.  The  actual  dimensions  depend  on  other  details. 


I 


62  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 

69.  Pedestal. — Cast-steel  pedestals,  as  shown  in  Fig. 
37  ( a ),  are  well  adapted  to  riveted  trusses.  The  top  half  is 
made  30  inches  long  and  a  little  wider  than  the  bottom  chord; 
in  this  case,  it  will  be  made  22  inches  wide.  It  is  bolted  to 
the  outstanding  legs  of  the  lower  flange  angle  by  means  of 
1-inch  bolts  p. 

The  height  of  the  pedestal  depends  on  the  allowable  dis¬ 
tance  from  the  base  of  the  rail  to  the  top  of  the  bridge  seat;  it 
is  desirable  to  keep  the  top  of  the  bridge  seat  above  high  water. 
When,  as  in  the  present  case,  high  water  is  considerably 
below  the  base  of  the  rail  (17  feet,  Art.  1),  the  total  height  r 
of  the  pedestal  should  be  made  about  the  same  as  its  length, 
and  the  pin  a'  placed  half  way  between  the  top  and  the  bot¬ 
tom.  For  a  truss  of  this  length,  a  pin  6  inches  in  diameter 
is  used. 

In  Fig.  37  (a),  the  part  bf  of  the  pedestal  in  contact  with 
the  sole  plate  h,  and  the  corresponding  part  b'  of  the  lower 
half  are  made  2  inches  thick;  the  part  d  in  contact  with  the 
pin  is  also  made  2  inches  thick.  The  two  bearing  surfaces 
of  each  half  of  the  pedestal  are  connected  by  a  vertical  web  q , 

3  inches  thick,  along  the  axis  of  the  pin  from  one  side  of 
the  pedestal  to  the  other,  and  by  webs  5,  If  inches  thick  and 

4  to  6  inches  apart.  Projections  /,  Fig.  37  (c) ,  are  cast  on 
the  inside  of  the  circular  part  of  the  pedestals;  they  fit  into 
circular  grooves  of  the  same  size  planed  out  of  the  pin,  and 
are  for  the  purpose  of  holding  the  pin  in  plac.e  and  also  pre¬ 
venting  halves  of  the  pedestal  from  moving  sidewise.  At 
one  end  of  the  bridge  the  bottom  of  the  pedestal  is  planed 
smooth,  and  a  steel  plate  i  inch  thick  is  placed  between  it 
and  the  masonry.  It  is  then  anchored  to  the  masonry  by 
bolts.  Fig.  37  ( e )  is  a  top  view  of  the  lower  half  of  the 
pedestal. 

At  the  expansion  end  of  the  bridge,  rollers  are  placed  under 
the  pedestal,  as  shown  at  u ,  Fig.  37  ( a ),  in  order  to  allow 
that  end  to  move  back  and  forth  as  the  temperature  changes. 

70.  Rollers. — The  allowable  pressure  per  linear  inch 
on  rollers  is  given  in  B.  S.,  Art.  29,  as  600  D.  Rollers  are 


I 


6b 


139-6*  Clear  between  Neat  Lines 


64  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  §79 


usually  made  from  3  to  6  inches  in  diameter,  and  about 
i  inch  is  left  between  each  two  rollers.  In  the  present  case, 
the  diameter  of  the  roller  will  be  made  4 1  inches;  6  rollers 
can  be  placed  under  the  pedestal,  which  is  30  inches  long. 
The  allowable  pressure  on  the  rollers  is  600  X  4.75  =  2,850 
pounds  per  linear  inch;  therefore,  the  number  of  inches 


required  is 


436,650 

2,850 


=  153.  As  there  are  6  rollers,  the 

length  of  each  must  be  ijp  =  25i  inches.  They  are  fastened 

together  so  as  to  form  a  roller  nest,  in  the  manner  shown  in 
Fig.  37  (/). 


BRIDGE-SEAT  PLAN 


71.  Bridge  Seat  for  Trusses. — Fig.  45  is  a  bridge- 
seat  plan  of  the  bridge  that  has  just  been  designed.  The 
distance  between  the  centers  of  the  pedestals  or  bedplates  a,  a 
is  shown  equal  to  the  span,  in  this  case  144  feet.  The  front 
of  each  pedestal  is  placed  1  foot  from  the  neat  line  of  the 
abutment,  which  makes  the  neat  line  2  feet  3  inches  from 
the  center  of  the  pedestal  at  each  end,  or  144  feet  —  2  feet 
3  inches  —  2  feet  3  inches  —  139  feet  6  inches,  between  neat 
lines. 

The  face  of  the  parapet  is  placed  6  inches  from  the  back 
edge  of  the  pedestal,  and  1  foot  9  inches  from  the  center  of 
the  pedestal;  this  makes  the  bridge  seat  for  the  truss  4  feet 
wide  from  neat  line  to  parapet.  It  is  customary  to  make 
the  bridge-seat  stone  2  feet  thick  for  a  span  of  this  length, 
and  to  have  it  project  about  6  inches  beyond  the  neat  line. 

The  distance  from  the  base  of  the  rail  to  the  top  of  the 
bridge  seat  is  found  by  adding  together  the  vertical  dis¬ 
tances  occupied  by  rollers,  pedestals,  stringers,  etc.  For 
the  fixed  end  shown  at  the  right,  these  distances  are  as 
follows: 

3  feet  9f  inches,  distance  from  the  base  of  the  rail  to  the 
bottom  of  the  bottom  chord,  Fig.  10; 

1  inch,  thickness  of  the  sole  plate  on  top  of  the  pedestal, 
Fig.  37  (b); 


§  7!)  DESIGN  OF  A  RAILROAD  TRUSS  BRIDGE  •  05 

2  feet  6  inches,  height  of  pedestal; 

1  inch,  thickness  of  bedplate  under  pedestal; 

6  feet  5i  inches,  total  distance  from  the  base  of  the  rail  to 
the  top  of  the  bridge  seat. 

At  the  expansion  end,  all  the  vertical  distances  are  the 
same  as  for  the  fixed  end,  except  that  the  rollers  and  bed¬ 
plates  occupy  inches,  or  6i  inches  more  than  the  i-inch 
bedplate  under  the  pedestal  at  the  fixed  end.  This  makes 
the  distance  from  the  base  of  the  rail  to  the  top  of  the  bridge 
seat  at  the  expansion  end  6  feet  —  5i  inches  +  64  inches 
=  6  feet  Ilf  inches,  as  shown  at  the  left  end. 

72.  Bridge  Seats  for  Stringers. — As  explained  in 
Art.  30,  the  bedplates  under  the  stringers  are  made 
20  inches  square.  It  is  customary  to  place  them  so  that 
their  centers  are  directly  opposite  the  centers  of  the  truss 
shoes.  A  separate  bridge  seat  and  parapet  are  built  up  on 
top  of  the  truss  seat  to  accommodate  the  stringers.  The 
parapet  is  usually  placed  about  4  inches  from  the  end  of  the 
stringer,  and  the  neat  line  6  inches  ahead  of  the  front  end  of 
the  bedplate,  making  the  stringer  bridge  seat  2  feet  6  inches 
wide  from  face  of  parapet  to  neat  line;  the  latter  is  11  inches 
from  the  neat  line  of  the  main  abutment. 

The  distances  from  base  of  rail  to  top  of  stringer  bridge 
seat  are  made  up  as  follows: 

72  inches  from  base  of  rail  to  top  of  stringer; 

2  feet  6i  inches,  depth  of  stringer  over  flange  angles; 

2  inches,  thickness  of  sole  plates  and  bedplates; 

3  feet  3f  inches,  total  distance  from  base  of  rail  to  top  of 
stringer  bridge. 


... 

I 


■ 


*.  • 

. 


~\  . 


WOODEN  BRIDGES 


INTRODUCTION 


USES  AND  TYPES  OF  WOODEN  BRIDGES 

1,  Disadvantages  of  Wood  for  Bridge  Construc¬ 
tion. — For  permanent  bridge  work  of  much  importance,  wood 
has  gone  out  of  use.  The  principal  reasons  for  this  are  the 
necessity  of  frequent  renewal,  the  increased  cost  of  timber 
and  decreased  cost  of  steel,  and  the  difficulty  and  delay  in 
securing  the  proper  quality,  sizes,  and  lengths  of  timber. 
In  addition  to  this,  the  danger  from  fire  has  played  an 
important  part  in  the  substitution  of  steel  for  wood  in  bridge 
building. 

2.  Conditions  to  Which  Wooden  Trusses  Are  Best 
Adapted. — Notwithstanding  the  above-mentioned  disad¬ 
vantages,  there  are  several  conditions  under  which  the  use 
of  timber  is  very  desirable.  Notable  among  these  are  the 
circumstances  that  render  advisable  the  use  of  pile  and 
frame  trestles,  a  trestle  being  practically  a  wooden  bridge. 
The  subject  of  trestles  is  fully  treated  in  another  Section  of 
this  Course,  and  need  not  be  further  considered.  Perhaps 
the  main  advantage  of  a  wooden  over  a  steel  bridge  is  its 
comparatively  low  first  cost.  The  percentage  of  saving  in 
first  cost  is  greater  in  short  than  in  long  spans,  and,  of 
course,  depends  on  the  relative  prices  of  wood  and  steel, 
these  prices  being  to  a  great  extent  governed  by  the  facili¬ 
ties  for  procuring  the  two  materials.  The  difference  in  the 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

l  80 


« 


80 


WOODEN  BRIDGES 


3 


percentage  of  saving  between  short  and  long  spans  is  due 
principally  to  the  increased  cost  of  the  ‘large-sized  timbers 
required  in  long  spans. 

3.  Wooden  trusses  are  also  used  for  work  of  a  temporary 
character,  such  as  a  temporary  road  around  a  site  on  which 
a  permanent  steel  structure  is  being  erected,  or  the  false 
work  necessary  for  the  support  of  traffic,  workmen,  and 
materials  during  the  erection  of  a  metal  bridge.  They  are 
also  frequently  used  in  irrigation  work  to  carry  flumes  and 
conduits  across  openings.  In  places  where  timber  is  easily 
accessible,  it  has  been  found  economical  in  many  cases  for 
highway  and  railroad  bridges  having  spans  from  100  to 
250  feet. 

4.  Combination  Bridges. — Bridges  are  occasionally 
constructed  entirely  of  wood,  except  the  bolts  used  to  con¬ 
nect  the  members.  In  the  great  majority  of  wooden  bridges, 
however,  only  the  compression  members  are  wood,  the  ten¬ 
sion  members  being  composed  of  eyebars  or  built-up  shapes, 
the  same  as  in  pin-connected  steel  trusses.  Such  bridges 
are  often  called  combination  bridges,  although  the  name 
wooden  bridge  is  usually  applied  both  to  all-wood  and  to 
combination  bridges. 

5.  Types  of  Wooden  Trusses. — The  principal  types  of 
trusses  in  which  timber  is  used  are  shown  in  Fig.  1.  In  this 
figure,  (a)  is  a  kingpost  truss,  and  ( b )  a  kingrod  truss. 
When  the  horizontal  members  ab  and  b  a'  serve  both  as 
chord  members  and  as  stringers  to  support  the  load  on 
the  floor,  these  trusses  are  called  trussed  stringers.  The 
trusses  shown  at  ( c )  and  (d)  are  queenpost  trusses,  and 
those  at  ( e )  and  (/)  are  queenrod  trusses.  Diagonals  are 
sometimes  inserted  in  the  center  panel,  as  at  {d)  and  (/), 
and  are  sometimes  omitted,  as  at  (e)  and  (e) .  When  the 
horizontal  members  ab,  b  b' ,  and  b'  a'  serve  both  as  chord 
members  and  as  stringers  to  support  the  load  on  the  floor, 
these  trusses  [(c),  (d) ,  (e),  and  (/)']  also  are  called  trussed 
stringers .  The  other  types,  (g),  (h) ,  and  (i)  are,  respect¬ 
ively,  Howe,  Pratt,  and  lattice  trusses. 

135—22 


4 


WOODEN  BRIDGES 


§80 


6.  Methods  of  Calculation. — As  a  rule,  the  methods 
employed  to  calculate  the  stresses  in  the  members  of  the 
trusses  shown  in  Fig.  1  are  the  same  as  those  explained  in 
the  various  parts  of  Stresses  in  Bridge  Trusses.  Special 
assumptions  are  made,  however,  for  some  of  the  types,  as 
will  be  explained  further  on. 


MATERIALS  AND  WORKING  STRESSES 


TIMBER 

7.  Kinds  of  Timber. — The  kind  of  timber  used  for  a 
wooden  bridge  depends  to  a  great  extent  on  the  locality. 
In  the  eastern  part  of  the  United  States,  yellow  pine  is 
employed  more  than  any  other  kind  of  timber;  white  oak 
and  white  pine  are  also  largely  used.  Spruce  is  used  to 
some  extent,  but  is  less  desirable  for  bridge  work  than  any 
of  the  other  kinds  mentioned.  In  the  western  part  of  the 
United  States,  Douglas,  or  Oregon,  fir,  which  is  very 
homogeneous  and  durable,  is  used  to  a  great  extent. 


WORKING  STRESSES  OF  TIMBER 
( Pounds  per  Square  Inch ) 


Kind  of 
Timber 

Kind  of  Stress 

Trans¬ 

verse, 

Stress 

Sb 

Com¬ 
pression 
on  Gross 
Section 

Tension 
on  Net 
Section 
St 

Shear¬ 

ing 

Along 

the 

Grain 

Ss 

Bearing 

Across 

the 

Grain 

Bearing 

Along 

the 

Grain 

sg 

Yellow  pine 

1,200 

8oo 

1,000 

80 

400 

1,250 

White  pine  . 

750 

500 

650 

50 

200 

800 

Spruce  .  .  . 

750 

6oo 

800 

60 

200 

800 

White  oak  . 

1,000 

700 

900 

100 

600 

1,250 

Douglas  fir  . 

1,200 

800 

1,000 

80 

400 

1,250 

80 


WOODEN  BRIDGES 


5 


8.  Allowable  or  Working  Stresses. — The  allowable 
or  working  stress  in  timber  depends  largely  on  the  seasoning. 
For  the  ordinary  timber  in  the  market,  fairly  well  seasoned, 
the  working  stresses  given  in  the  table  on  page  4  may  be 
used  for  bridge  work. 

1.  Transverse  Stress. — The  allowable  transverse  stresses 
given  in  the  table  are  the  greatest  allowable  values  of  St,  in 
pounds  per  square  inch,  as  found  by  the  formula 


Me 


explained  in  Strength  oh  Materials. 

2.  Compression. — The  allowable  compressive  stresses 
given  in  the  table  are  the  greatest  allowable  values  of  sCJ 
in  pounds  per  square  inch,  as  found  by  the  formula 


and  are  for  members  whose  greatest  length  is  not  greater 
than  eight  times  the  least  side  or  diameter.  For  members 
whose  length  is  greater  than  eight  times  the  least  width,  the 
working  compressive  stress  s/,  in  pounds  per  square  inch,  is 
obtained  by  means  of  the  following  formula:  . 


5, 


in  which  sc  —  value  given  in  the  tabl^; 


l  —  length  of  the  member; 
d  =  diameter  or  least  side. 

For  example,  if  the  length  of  a  yellow-pine  column  is 
15  feet,  and  the  cross-section  is  10  in.  X  12  in.;  then,  since 
the  least  side  is  10  inches  and  the  value  of  sc  given  in  the 
table  is  800,  the  allowable  working  stress  is 


800 


=  348  lb.  per  sq.  in. 


3.  Tension. — The  allowable  tensile  stresses  given  in  the 
table  are  the  greatest  allowable  stresses  st  as  found  by  the 


formula 


6 


WOODEN  BRIDGES 


80 


in  which  A  is  the  net  area  of  the  member  after  deducting 
bolt  holes,  cuts  at  connections,  etc. 

4.  Shearing  Along  the  Grain. — The  working  stresses  ss 
given  in  the  table  for  shearing  along  the  grain  are  the  greatest 
allowable  longitudinal  shearing  stresses  at  the  neutral  axis  of 
a  beam.  For  a  rectangular  beam,  the  intensity  of  shear,  as 
found  by  the  formula 

-  ZZ 

S‘  2b  h 

must  not  exceed  the  working  stress  given  in  the  table.  In 
this  formula,  V  is  the  greatest  external  shear  on  the  beam, 
and  b  and  h  are  the  width  and  depth  of  the  beam  at  the  sec¬ 
tion  of  greatest  shear.  In  addition,  the  tabular  values  are  the 
maximum  allowable  stresses  at  the  §nds  of  bridge  members 
where  they  connect  to  others,  as  will  be  explained  presently. 

5.  Bearhig  Across  the  Grain. — The  allowable  working 
stresses  sa  given  in  the  table  for  bearing  across  the  grain  are 
the  greatest  allowable  intensities  of  bearing  on  the  sides  of 
members  where  other  members  at  right  angles  to  the  first 
connect  to  them. 

6.  Bearing  Along  the  Grain. — The  allowable  working 
stresses  ss  given  in  the  table  for  bearing  along  the  grain  are 
the  greatest  allowable  intensities  of  bearing  at  the  ends  of 
compression  members,  where  they  rest  on  other  members. 


METALS 

9.  Steel. — Steel  rods  and  shapes  are  commonly  used  for 
the  metal  portions  of  combination  bridges,  and  when  so  used 
are  designed  in  the  same  way  as  for  steel  bridges.  The 
working  stresses  are  the  same  as  those  given  in  Bridge 
Specifications. 

10.  Wrought  Iron. — Although  wrought  iron  has  been 
almost  entirely  superseded  by  steel,  it  is  still  used  to  a  slight 
extent  for  the  metal  portions  of  combination  bridges.  When 
so  used,  the  members  are  designed  in  the  same  way  as  for 
steel  bridges,  and  the  allowable  working  stresses  may  be  taken 
as  75  per  cent,  of  those' given  for  steel  in  Bridge  Specifications. 


§80 


WOODEN  BRIDGES 


7 


KINGPOST  AND  KINGROD  TRUSSES 

11.  Trusses  of  the  kingpost  and  kingrod  types  are  espe¬ 
cially  useful  for  short  spans  that  are  too  long  for  the  use  of 
simple  beams.  They  may  be  made  as  long  as  25  or  30  feet. 
On  account  of  the  lighter  loads,  they  can  be  used  for  longer 
spans  for  highway  than  for  railroad  bridges. 

12.  Description  of  Kingpost  Truss. — Fig.  2  repre¬ 
sents  the  simplest  form  of  kingpost  truss.  It  consists  of  a 


top  chord  a  a,  a  vertical  kingpost  b ,  which  supports  the  top 
chord  at  the  center,  and  a  bent  rod  cc  connecting  the  bottom 
of  the  kingpost  with  the  ends  of  the  top  chord.  The  king¬ 
post  is  held  in  position  at  the  top  by  means  of  a  wooden 
pin  or  iron  drift  bolt  £,  and  also  by  being  set  or  framed  into 
the  top  chord.  At  the  bottom  of  the  kingpost,  a  casting  g 
distributes  the  pressure  of  the  rod  cc  over  the  end  of  the 
post;  the  bottom  of  the  casting  is  grooved  in  order  to  afford 
the  rod  a  better  bearing.  At  the  ends  of  the  truss,  the 
rod  c  c  passes  through  plates  <?,  e  that  bear  on  the  end  of  the 
top  chord;  the  ends  of  the  rod  are  held  in  place  by  nuts  /,  /. 
The  ends  of  the  chord  a  a  usually  rest  on  timber  blocking  J,j 
that  is  supported  by  the  bridge  seat  i  or  bent  on  which  the 
truss  rests.  The  distance  /  between  the  centers  of  the 
blocking  on  which  the  truss  rests  is  the  span.  The  post  b  is 


8 


WOODEN  BRIDGES 


80 


at  the  center  of  the  span,  making  each  panel  equal  to  -. 

z 

» 

The  distance  h  from  the  center  of  the  horizontal  chord  to 
the  intersection  of  the  inclined  members  with  the  kingpost 
is  called  the  height  of  the  truss. 


13.  In  some  cases,  the  top  chord  simply  consists  of  one 
timber,  and  the  rod  passes  through  it.  In  other  cases,  there 
are  two  or  more  timbers,  and  one  less  or  one  more  rod  than 
there  are  timbers,  the  rods  passing  between  the  timbers  and 
in  some  cases  outside  of  them  at  each  side.  Fig.  3  shows 

the  arrangement  at 
the  end  when  there 
are  two  timbers  and 
one  rod.  Large  cast- 
iron  washers  c  hold 
the  timbers  /,  /, 
Fig.  3  (b) ,  far  enough 
apart  to  allow  the 
rod  g  to  pass  between 
them,  and  f-inch 
bolts  e,  e ,  spaced  2  or 


_ 

!  T  ! 

; 

i  i  i 

/ - 

-e 

!j 

y 

5  "  r~ 

;  i 

1  "(ill 

nrr 

To  ** 

-£-V  M 

li 

•V“  11 

.  ,  II  ■  ■  .  . 

!  T  c' 

1  ! 

^ i 4 

- * - 

i» 

m 

n 

(by 


3  feet  apart,  hold  the 
timbers  together  and 
make  them  act  as 
one  piece.  The  holes 
for  these  bolts  are 
usually  bored  i  inch  less  in  diameter  than  the  diameter  of  the 
bolt,  and  the  bolts  are  driven  in;  this  makes  them  fit  tight 
in  the  wood.  Cast-iron  washers  d ,  d  are  placed  on  the  ends 
of  the  bolts  to  prevent  the  heads  and  nuts  from  sinking  into 
the  wood. 


14.  Description  of  Kingrod  Truss. — When  there  is 
not  sufficient  room  for  the  kingpost  and  bent  rod  to  project 
below  the  floor,  the  kingrod  truss  shown  in  Fig.  4  is  used. 
In  this  truss,  the  bottom  chord  a  a  is  composed  of  wood, 
and  is  horizontal;  the  kingrod  b  is  made  of  iron  or  steel,  and 
the  inclined  members  cyc,  commonly  called  struts,  are 


§80 


WOODEN  BRIDGES 


9 


made  of  wood.  The  kingrod  passes  through  the  bottom 
chord  and  supports  its  center,  the  plate  e  and  the  nut  /  help¬ 
ing  to  hold  the  chord  in  place.  The  top  of  the  rod  passes 
through  and  between  the  ends  of  the  struts  c ,  c .  The  nut  /' 
and  plate  ef  hold  this  end  of  the  rod  in  place  and  transmit 
the  stress  in  the  rod  to  the  struts.  At  the  ends  of  the  truss, 


the  top  of  the  bottom  chord  is  notched,  and  the  lower  ends 
of  the  struts  are  framed  so  as  to  fit  into  these  notches. 
To  assist  in  transmitting  the  stresses  from  the  struts  to  the 
bottom  chord,  each  strut  is  connected  to  the  chord  by 
inclined  bolts  g,g . 

15.  Method  of  Calculating  the  Stresses. — The 
method  of  calculating  the  stresses  in  the  kingpost  or  king- 
rod  truss  depends  on  the  manner  in  which  the  load  is  applied. 
The  two  usual  conditions  of  loading  will  be  discussed;  they 
are:  (1)  when  the  load  is  applied  to  the  truss  at  the  center 
by  a  floorbeam;  and  (2)  when  the  load  is  applied  along  the 
horizontal  chord,  the  latter  acting  both  as  a  stringer  and  as  a 
chord.  Since  the  kingrod  truss  is  simply  a  kingpost  truss 
inverted,  the  same  methods  apply  to  both,  and  only  the 
kingpost  truss  will  be  discussed  here. 

16.  Case  I. — When  the  load  is  applied  to  the  truss  as  a 
single  load  at  the  center  joint  by  means  of  a  floorbeam,  as 
shown  in  outline  in  Fig.  5,  the  stresses  in  the  members  are 


10 


WOODEN  BRIDGES 


80 


all  direct  stresses,  and  can  be  found  by  the  methods  explained 
in  Stresses  in  Bridge  Trusses.  In  Fig.  5,  h  is  the  vertical 
distance  between  the  center  of  the  horizontal  chord  and  the 
center  of  the  bent  rod  at  the  center  of  the  span,  and  /  is  the 
distance  between  the  centers  of  the  blocking,  which  should 
be  directly  under  the  intersections  of  the  inclined  members 

with  the  horizontal 
chord. 


17.  Case  II.— 
When  the  load  is 
applied  at  every  point 
along  the  truss,  as 
shown  in  outline  in  Fig.  6,  the  stresses  in  the  vertical  and 
inclined  members  are  direct  stresses;  but  in  the  horizontal 
chord  there  is,  in  addition  to  the  direct  stress,  a  bending 
moment  due  to  the 
loads.  This  moment  is 
positive  at  sections 
from  a  and  a’  to  sections 
near  b,  and  is  negative 
at  b  and  for  a  short  dis¬ 
tance  at  each  side  of  b. 

The  formulas  for  the 
stresses  in  the  members  for  this  condition  of  loading  are 
given  here  without  their  derivation,  which  requires  the  use 
of  advanced  mathematics. 

In  these  formulas, 

W  —  total  load,  in  pounds,  uniformly  distributed  on  the  truss; 
/  =  span,  in  inches; 

h  =  distance,  in  inches,  from  the  center  of  the  bent  rod  to 
the  center  of  the  top  chord  at  the  center  of  the  span; 
H  —  angle  that  the  inclined  member  makes  with  the 
horizontal; 

bf  —  net  width,  in  inches,  of  the  horizontal  chord; 
d’  —  net  depth,  in  inches,  of  the  horizontal  chord. 

In  computing  the  net  width  and  net  depth,  it  is  necessary 
to  deduct  from  the  gross  width  and  depth,  respectively,  the 


§80 


WOODEN  BRIDGES 


11 


amount  of  section  removed  for  the  drift  bolt  k,  Fig.  2, 
usually  1  inch  in  width,  and  for  the  material  removed  at  the 
top  of  the  post  b  for  its  connection,  usually  about  i  inch 
deep.  Referring  to  Fig.  6,  the  stresses,  in  pounds,  are  as 
follows: 

Total  direct  stress  in  b  B: 


c  5 IV 

=  — — -,  compression 

8 

Total  direct  stress  in  aB  and  B  ar : 

c  5  W  rr  . 

S2  =  — -  esc  //,  tension 

Total  direct  stress  in  ab  and  ba' : 


(1) 

(2) 


= 


5  W  l 
32  h 


,  compression 


Maximum  bending  moment  on  a  a'  ( at  b) : 

M  —  WJc  inch-pounds 
32 

Maximum  intensity  of  stress  o?i  a  a'  (at  b): 


s  = 


Wl 


(3) 


(4) 


32  h  b'  dr 


X  [5  d'  +  6  h\  lb.  per  sq.  in.,  compression  (5) 


In  designing  the  horizontal  chord,  it  is  necessary  first  to 
assume  a  cross-section,  and  then  calculate  the  intensity  of 
stress  by  means  of  formula  5.  If  the  actual  stress  is  greater 
than  the  allowable  stress  sj  as  found  by  the  formula  in 
Art.  8,  or  much  less,  the  section  is  revised,  and  the  intensity 
of  stress  is  again  computed  by  formula  5.  This  process  is 
repeated  until  the  proper  section  is  found. 


Example  1. — In  the  kingpost  truss  shown  in  outline  in  Fig.  6,  let 
the  span  be  20  feet;  the  height,  5  feet,  and  the  weight  w  per  linear 
foot,  2,000  pounds.  To  find:  (a)  the  total  direct  stress  in  b  B\  (b)  the 
total  direct  stress  in  Ba'\  (r)  the  total  direct  stress  in  ab\  ( d )  the 
greatest  bending  moment  on  a  a'. 


Solution. — Since  the  weight  per  linear  foot  is  2,000  lb.  and  the 
length  is  20  ft.,  the  total  load  IV  on  the  truss  is  2,000  X  20  =  40,000  lb. 
Also,  /  =  20  X  12  =  240  in.,  and  h  —  5  X  12  =  60  in.  4 
i  (a)  The  stress  in  b  B  is  found  by  formula  1.  Substituting  the 
proper  value  for  W  gives 


Si  = 


5  X  40,000 


=  25,000  lb.,  compression.  Ans. 


8 


12  WOODEN  BRIDGES  §80 


(b)  The  total  direct  stress  in  B  a'  is  found  by  formula  2.  In  the 
present  case, 


esc  H  = 
Therefore, 


h 


60 


=  2.236 


5,  =  5  x  4°’Q0Q  x  2.236  =  27,950  lb.,  tension.  Ans. 

16 

(r)  The  total  direct  stress  in  a  b  is  found  by  formula  3: 

c  5  X  40,000  X  240  0_  nn„  .  . 

S3  =  - — — - =  2o,000  lb.,  compression.  Ans. 

X  60 

( d )  The  bending  moment  on  a  a'  is  greatest  at  b,  and  its  value  is 
found  by  formula  4: 


M 


40,000  X  240 
32 


300,000  in. -lb.  Ans. 


Example  2. — If  the  member  a  a'  is  composed  of  two  timbers 
8  inches  wide  and  16  inches  deep,  what  is  the  greatest  intensity  of 
stress  on  the  section? 

Solution. — To  get  the  net  width,  it  is  necessary  to  deduct  1  in. 
from  the  width  of  each  stick  to  allow  for  the  decrease  in  section  by  the 
holes  for  the  drift  bolts;  this  leaves  7  in.  for  the  net  width  of  each,  and 
14  in.  for  the  net  width  b'  of  the  two.  Deducting  \  in.  from  the  depth 
to  allow  for  the  decrease  for  the  connection  of  the  kingpost  leaves  the 
net  depth  d'  —  15ijr  in.  The  maximum  intensity  of  stress  is  found  by 
formula  5: 

40,000  X  240  , 

5  "  32>T60  X  14  X  15.5  s  X  (5  X  ,15'5  +  6  X  60) 

=  650  lb.  per  sq.  in.,  compression.  Ans. 


18.  Example  of  Kingrod  Bridge. — Fig.  7  shows  a 
small  highway  bridge  composed  of  one  layer  of  floor  plank 
2  inches  thick,  the  floor  joists  /,  the  floorbeam  g,  and  the 
kingrod  trusses.  In  the  figure,  (a)  is  the  plan,  (b)  is  the 
elevation,  and  (c)  shows  the  connection  of  the  floorbeam  g 
to  the  kingrod  e  of  the  truss.  The  floorbeams  are  continued 
4  feet  3  inches  beyond  the  truss  on  each  side,  and  inclined 
struts  z,  usually  4  in.  X  6  in.,  are  placed  between  the  end  of 
the  floorbeam  and  the  top  joint  of  the  truss  to  hold  it  in 
place.  This  is  a  very  economical  and  serviceable  bridge  for 
localities  to  which  it  is  adapted. 


6x6  Fast 


13 


14 


WOODEN  BRIDGES 


80 


EXAMPLES  FOR  PRACTICE 

1.  The  panel  load  W  of  the  truss  shown  in  outline  in  Pig.  5  is 
20,000  pounds.  If  the  span  is  20  feet,  and  the  height  is  4  feet,  what 
is  the  direct  stress  in  the  top  chord?  Ans.  25,000  lb.,  compression 

2.  The  load  w  per  linear  foot  on  the  truss  shown  in  outline  in 
Fig.  6  is  2,400  pounds.  If  the  span  is  25  feet,  and  the  height  is  5  feet, 
what  is  the  direct  stress  in  the  member  b 

Ans.  37,500  lb.,  compression 

3.  What  is  the  direct  stress  in  the  member  B  a'  of  the  truss  referred 

to  in  example  2?  Ans.  50,500  lb.,  tension 

4.  What  is  the  direct  stress  in  the  member  b  a'  of  the  truss  referred 

to  in  example  2?  Ans.  46,900  lb.,  compression 

5.  What  is  the  greatest  bending  moment  on  the  top  chord  of  the 

truss  referred  to  in  example  2?  Ans.  562,500  in. -lb. 


QUEENPOST  AND  QUEENROD  TRUSSES 

19.  Description  of  the  Queenpost  Truss. — Fig.  8 
represents  a  queenpost  truss,  which  is  similar  to  the  king¬ 
post  truss,  except  that  the  former  has  three  panels  instead 
of  two.  The  inclined  struts  e>  e  are  placed  in  the  center 
panel  to  provide  for  the  shear  in  that  panel;  the  top  chord  a  a 
is  made  continuous  from  end  to  end.  The  rod  cc  is  some¬ 
times  made  in  one  piece,  and  sometimes  in  two  pieces;  in 
the  latter  case,  a  turnbuckle  is  inserted  in  the  center  panel. 
The  castings  /,  /  at  the  bottoms  of  the  posts  provide  a  bear¬ 
ing  area  for  the  posts  and  also  for  the  ends  of  the  inclined 
struts.  The  bottoms  of  the  castings  are  grooved  in  order  to 
afford  the  rods  a  better  bearing. 

20.  Description  of  tlie  Queenrod  Truss. — When 
there  is  not  sufficient  room  for  the  posts  and  rods  to  project 
below  the  floor,  the  queenrod  truss  shown  in  Fig.  9  is  used. 
This  truss  is  similar  in  every  way  to  the  kingrod  truss, 
except  that  there  are  three  panels  in  the  former  instead  of 
two.  Castings  g  are  bolted  to  the  upper  ends  of  the  inclined 
struts,  to  provide  a  bearing  for  the  upper  ends  of  the 
inclined  web  members  <?,  e  in  the  center  panel.  Instead  of 


§80 


WOODEN  BRIDGES 


17 


the  lower  end  of  the  inclined  strut  at  the  end  being  bolted  to 
the  chord  by  two  bolts,  as  in  Fig.  4,  the  strap  z,  Fig.  9,  is 
sometimes  used.  This  is  a  flat  piece  of  iron  or  steel  about 
2j  in.  X  t  in.,  bent  over  the  lower  end  of  the  strut  and  bolted 
to  the  sides  of  the  chord. 

21.  Other  Forms  of  Queenpost  and  Queenrod 
Trusses. — In  addition  to  the  forms  shown  in  Figs.  8 
and  9,  queenpost  and  queenrod  trusses  are  frequently 
built  as  shown  in  Figs.  10  and  11,  the  inclined  struts  in 
the  center  panel  being  omitted.  The  shear  in  that  panel 
is  then  resisted  by  the  continuous  chord  a  a  acting'  as  a 
beam,  as  will  be  explained  presently.  In  the  queenpost 
truss,  or  trussed  stringer,  shown  in  Fig.  10,  a  horizontal 
strut  k  is  usually  inserted  between  the  lower  ends  of  the 
posts  in  order  to  prevent  them  from  sliding  toward  each 
other  on  the  rods. 

22.  Method  of  Calculating  the  Stresses. — The 
stresses  in  the  members  depend  on  the  type  of  truss  and 
the  manner  in  which  the  loads  are  applied.  The  difference 
between  the  queenrod  and  the  queenpost  truss  is  the  usual 
difference  between  a  through  and  a  deck  truss,  and  only  the 
former  will  be  here  considered.  There  are  four  conditions 
of  loading  that  require  to  be  taken  into  account.  They  are 
as  follows:  (1)  when  the  load  is  applied  to  the  truss  shown 
in  Fig.  9  by  floorbeams  at  the  panel  points;  (2)  when  the 
load  is  applied  to  the  truss  shown  in  Fig.  9  all  along  the 
bottom  chord,  this  member  acting  as  a  beam  to  support 
the  loads  in  the  panels  and  also  as  a  member  of  the  truss; 
(3)  when  the  load  is  applied  to  the  truss  shown  in  Fig.  11 
by  floorbeams  at  the  panel  points;  (4)  when  the  load  is 
applied  to  the  truss  shown  in  Fig.  11  all  along  the  bottom 
chord,  this  member  acting  as  a  beam  to  support  the  loads  in 
the  panels  and  also  as  a  member  of  the  truss. 

23.  Case  I. — The  condition  of  loading  for  Case  I  is 
shown  in  Fig.  12.  Since  there  are  no  external  forces  acting 
on  the  truss  except  the  panel  loads  Wt  and  W*  and  the  reac¬ 
tions  R ,  mid  A\,  the  stresses  in  all  the  members  are  direct 


18 


WOODEN  BRIDGES 


80 


stresses,  and  can  be  found  by  any  of  the  methods  explained 
in  Stresses  in  Bridge  Trusses. 


24.  Case  II. — The  condition  of  loading  for  Case  II  is 
shown  in  Fig.  13.  The  external  forces  are  the  reactions  Rx 
and  and  the  uniform  load  per  linear  foot.  In  addition  to 
the  direct  stress  in  the  bottom  chord  abb'  a' ,  there  is  a  bend¬ 
ing  moment  on  this  member  due  to  the  loads  applied  between 
the  panel  points.  On  this  account,  the  stresses  in  the 
members  are  somewhat  different  from  those  in  Case  I.  The 
greatest  stresses  in  the  members  are  found  approximately 


by  the  formulas  given  below,  which  are  derived  by  the  use 
of  advanced  mathematics.  In  these  formulas, 

W  =  total  load  on  the  truss,  in  pounds; 
l  —  span,  in  inches; 

h  —  distance,  in  inches,  between  the  centers  of  the  chords; 
H  —  angle  between  the  inclined  members  and  the  horizontal, - 
bf  =  net  width  of  the  continuous  chord  abb'  a!\ 
d'  =  net  depth  of  the  continuous  chord  abb'  a'. 

The  formulas  are  as  follows,  the  stresses  being  in  pounds: 
Total  direct  stress  in  b  B  and  b'  B' : 

Sr  •=  .367  W,  tension  (1) 

Total  direct  stress  hi  a  B  and  B'  a' : 

Sr  —  .367  W  esc  //,  compression  (2) 


80 


WOODEN  BRIDGES 


19 


Total  direct  stress  in  b  B'  and  b'  B: 

W 


S2  - 


9 


esc  H ,  compression 


Total  direct  stress  in  B  B'  and  in  ab  bf  af : 

.122  Wl 


h 


(3) 


(4) 


The  stress  S4  is  compression  in  B  B'  and  tension  in  a  b  b'  a' . 
Maximum  bending  moment  on  a  b  b'  a': 


M  —  ——  inch-pounds 
90 

Maximum  intensity  of  stress  on  abb'  a': 
Wl 


s  — 


90  h  V  dr 


(11  d’  +  6  h)  lb.  per  sq.  in.,  tension 


(5) 


(6) 


B  B 

f 

h 

b  1  b ' 

It 

i  \ 

E  1 

l 

i  t 

3  1 

m  3 

7 

w2  3 

Fig.  14 


25.  Case  III. — The  conditions  of  loading  that  must  be 
considered  in  this  case  are  shown  in  Figs.  14  and  15.  In 
Fig.  14,  both  panel 
points  are  loaded  (  Wx 
and  W2),  and  when 
the  loads  are  equal, 
as  is  usually  the  case, 
the  stresses  in  the 
members  are  all  direct 
stresses,  and  can  all 
be  found  by  the  principles  explained  in  Stresses  in  Bridge 
Trusses.  This  loading  causes  the  greatest  direct  stresses  in  all 
the  members,  and  controls  the  size  of  all  the  members  except 

the  chord  ab  b'  a' . 

The  loading  shown 
in  Fig.  15  causes  a 
a  bending  moment  in 
the  member  abb'  a', 
Ro  so  that  in  some  cases 
this  condition  of  load¬ 
ing  controls  the  size 
of  that  member.  In  Fig.  15  there  is  but  one  panel  point 
loaded;  part  of  the  load  is  supported  by  the  truss,  and  the 
remainder  by  the  member  abb' a'  acting  as  a  beam.  When 

135—23 


B 


B 


R 


*  Jr 

* 

S 

s 

/ 

- - - 

Tt 

h  j 

// 

b  l 

~~~~i  '  ,n 

3 

3  r\ 

3 

1V2 

t 

Fig.  15 


20 


WOODEN  BRIDGES 


80 


the  truss  deflects,  it  assumes  a  position  similar  to  that 
shown  in  Fig.  15  in  dotted  lines.  It  is  impossible  to 
tell  with  accuracy  how  much  of  the  load  is  supported  by 
the  truss,  and  how  much  by  the  lower  chord  as  a  beam; 
it  is  customary  to  assume,  however,  that  one-half  the  panel 
load  is  supported  by  the  truss,  and  one-half  by  the 
member  abb'  a!  as  a  beam.  On  this  assumption,  the  stresses 
in  abb'  a'  are  as  follows: 

Total  direct  stress  in  abb'  a': 

S  =  pounds,  tension  (1) 

6  h 

Bendi?ig  moment  in  abb'  a': 

M  —  inch-pounds  (2) 

Maximum  intensity  of  stress  in  a  b  b'  a': 

s  —  ■  (d'  -f  2  h)  lb.  per  sq.  in.,  tension  (3) 

~  6  h  b’ d n 


Fig.  16 


26.  Case  IV. — The  condition  of  loading  that  needs  to 
be  considered  in  this  case  is  shown  in  Fig.  16.  In  addition 

to  the  direct  stress  in 
the  bottom  chord, 
there  is  a  bending 
moment  due  to  the 
loads  that  are  applied 
to  the  truss  between 
the  panel  points.  This 
condition  is  similar  to 
that  shown  in  Fig.  13,  and  discussed  under  Case  II.  The 
stresses  in  the  members  of  Fig.  16  can  be  found  by  means  of 
the  formulas  given  under  Case  II.  When  the  truss  is  partly 
loaded,  part  of  the  load  is  carried  to  the  abutments  by  the 
truss  and  part  by  the  bottom  chord  acting  as  a  beam  in  the 
same  way  as  explained  under  Case  III  and  illustrated  in 
Fig.  15.  In  this  case,  however,  the  stresses  in  the  members 
when  the  truss  is  fully  loaded,  as  shown  in  Fig.  16,  are 
greater  than  when  the  truss  is  partly  loaded;  hence,  the  latter 
condition  of  loading  need  not  be  considered. 


80 


WOODEN  BRIDGES 


21 


27.  The  formulas  given  in  the  preceding  articles  give  the 
stresses  in  the  members  of  the  various  types  of  queenrod 
trusses.  The  same  formulas  can  be  used  for  the  stresses  in 
the  members  of  the  queenpost  truss;  the  results  will,  in  gen¬ 
eral,  be  numerically  the  same  as,  but  opposite  in  sign  to,  those 
found  for  the  corresponding  members  of  the  queenrod  truss. 

Example  1. — In  the  queenrod  truss  shown  in  Fig.  13,  let  the 
weight  w  be  1,800  pounds  per  linear  foot,  the  length  30  feet,  and  the 
height  6  feet.  To  find:  (a)  the  total,  load  on  the  truss;  (b)  the  total 
direct  stress  in  b  B\  (c)  the  total  direct  stress  in  a  B;  ( d )  the  total 
direct  stress  in  abb'  a ( e )  the  bending  moment  on  abb'  a'. 


Solution. — (a)  Since  the  load  zv  per -linear  foot  is  1,800  lb.,  and 
the  length  is  30  ft.,  the  total  load  W  on  the  truss  is  1,800  x  30 
=  54,000  lb.  Ans. 

(b)  The  total  direct  stress  in  b  B  is  found  by  formula  1  of  Art.  24. 
Here,  W  =  54,000  lb.,  and,  therefore, 

S’,.  =  .367  X  54,000  =  19,800  lb.,  tension.  Ans. 

(c)  The  total  direct  stress  in  a  B  is  given  by  formula  2  of  Art.  24. 

VlO2  4-  62 

Here,  W  =  54,000  lb.,  esc  H  —  - - - =  1.944,  and,  therefore. 


S2  =  .367  X  54,000  X  1.944  =  38,500  lb.,  tension.  Ans. 

( d )  The  total  direct  stress  in  a  b  b' a'  is  given  by  formula  4  of 
Art.  24.  Here,  zv  =  54,000  lb.,  I  —  (30  X  12)  in.,  and  h  —  (6  X  12)  in. 

Therefore, 


.122  X  54,000  X  30  X  12 


=  32,900  lb.,  tension.  Ans. 


6  X  12 

(<?)  The  bending  moment  on  abb'  a'  is  given  by  formula  5  of 
Art.  24.  Here,  W  =  54,000  lb.,  and  /  =  (30  X  12)  in.  Therefore, 


M  - 


54,000  X  30  X  12 
90 


=  216,000  in. -lb.  Ans. 


Example  2. — If  the  member  abb'  a'  in  the  preceding  example  is 
composed  of  two  sticks  each  7  in.  X  14  in.  in  cross-section,  what  is  the 
maximum  intensity  of  stress  in  the  member? 


Solution. — The  maximum  intensity  of  stress  is  given  by  formula  G 
of  Art.  24.  In  the  present  case,  W  =  54,000  lb.,  /  =  (30  X  12)  in., 
and  //  =  (6  X  12)  in.  It  will  be  assumed  that  the  width  of  each  sticl?  is 
decreased  1  in.  by  connection  bolts,  making  the  net  width  b'  of  the 
two  combined  2  X  (7  —  1)  =  12  in.  It  will  be  assumed  that  the  depth 
is  decreased  \  in.  at  connections,  leaving  the  net  depth  d'  =  14  —  \ 


=  13.5 


in.  Substituting  in  the  formula, 
54,000  X  30  X  12 


s  = 


90  X  6  X  12  X  12  X  13. 52 
=  796  lb.  per  sq.  in. 


X  (11  X  13.5  +  6  X  72) 
tension.  Ans. 


m* 


* 


22 


I 


I 


§80 


WOODEN  BRIDGES 


23 


28.  Queenrod  Bridge  Without  Diagonals. — Fig.  17 
shows  a  small  railroad  bridge  composed  of  two  queenrod 
trusses  with  no  diagonals  in  the  center  panel:  (a)  is  the 
elevation  of  the  bridge,  (b)  is  the  end  view,  and  (c)  is  the 
detail  of  the  casting  that  holds  the  ends  of  the  members  in 
place  at  the  top  of  the  truss.  In  this  bridge,  there  are  no 
stringers  or  floorbeams;  the  ends  of  the  ties  d,  d  rest  directly 
on  top  of  the  bottom  chord,  and  are  notched  to  hold  them 
in  position.  Bottom  lateral  braces  /,  t  are  inserted  between 
the  trusses.  Bottom  transverse  struts  <?,  usually  about 
10  in.  X  12  in.  X  30  ft.,  are  placed  under  the  trusses  and 
extended  a  short  distance  beyond  the  trusses  at  each  side  of 
the  bridge.  Inclined  struts  /, /,  usually  about  6  in.  X  8  in., 
connect  the  ends  of  the  transverse  struts  with  the  top  chord 
of  the  trusses  in  order  to  hold  the  trusses  in  position.  This 
form  of  bridge  is  very  serviceable  for  temporary  purposes 
on  a  railroad  operating  light  locomotives  and  cars. 


EXAMPLES  FOR  PRACTICE 

•1.  In  the  queenrod  truss  shown  in  Fig.  16,  let  w  =  1,200  pounds 
per  linear  foot,  /  =  36  feet,  and  h  =  6  feet.  What  is  the  total  direct 
stress  in  the  member  aB?  Ans.  35,450  lb.,  compression 

2.  What  is  the  total  direct  stress  in  the  member  b  B  of  the  truss 

referred  to  in  example  1?  Ans.  15,850  lb.,  tension 

3.  In  the  queenrod  truss  shown  in  Fig.  15,  let  W2  =  10,000  pounds, 
/  =  33  feet,  and  h  =  6  feet.  What  is  the  total  direct  stress  in  a  b  b'  a'  ? 

Ans.  9,170  lb.,  tension 

4.  What  is  the  bending  moment  on  the  member  abb'  a'  of  the 

truss  referred  to  in  example  3?  Ans.  220,000  in. -lb. 


24 


WOODEN  BRIDGES 


§80 


THE  HOWE  TRUSS 

29.  General  Description. — The  method  of  calculating 
the  stresses  in  the  members  of  the  Howe  truss  was  explained 
in  Stresses  in  Bridge  Trusses ,  Part  2.  The  general  descrip¬ 
tion  of  the  truss,  as  built  in  wood,  and  the  details  of  the 
connections  are  all  that  it  is  necessary  to  give  here. 

30.  Fig.  18  is  an  elevation  of  a  wooden  Howe  truss. 
The  top  and  bottom  chords  and  the  inclined  web  members 
are  composed  of  timbers;  the  vertical  rods  are  composed  of 
wrought  iron  or  steel.  The  chords  are  usually  composed 
of  several  timbers  of  nearly  the  same  size;  these  timbers  are 
commonly  called  sticks.  The  inclined  web  members  and 
the  verticals  are  connected  to  each  other  and  to  the  chord 
by  means  of  a  cast-iron  or  cast-steel  block,  commonly  called 
a  chord  block,  as  shown  at  a  be  in  Fig.  19  ( a ).  This  figure 
shows  a  bottom  chord  joint;  the  block  a  b  c  is  set  on  top  of 
the  chord,  and  lugs  e,  e ,  cast  on  the  block,  fit  into  grooves  of 
the  same  size  in  the  top  of  the  chord.  The  vertical  rods  /,  i 
pass  through  the  chord  block  and  between  the  several  sticks 
that  compose  the  chord;  they  are  held  in  plate  by  means  of 
the  plates  g  and  nuts  h  on  the  bottom  of  the  rods.  The 
upper  surface  of  the  chord  block  is  inclined  on  each  side  of 
the  vertical  rod  so  as  to  give  the  diagonals  Ed'  and  d'  C'  a 
square  bearing.  In  some  cases,  lugs  z,  i  are  cast  on  the 
inclined  surfaces  of  the  casting  so  that  the  inclined  mem¬ 
bers  will  remain  in  place.  The  chord  blocks  are  made  just 
large  enough  to  give  the  inclined  members  the  proper 
width  of  bearing.  They  are  not  made  solid,  but  with  hol¬ 
low  spaces  to  decrease  the  weight.  The  outside  shell  is 
usually  made  from  1  inch  to  1  i  inches  thick.  The  lugs  e}  e 
are  seldom  made  more  than  1  inch  deep  or  more  than 
2  inches  wide.  The  plates  ^  are  made  from  1  to  2  inches  in 
thickness. 


4 


*4 


4 


4 


4 


*4 


Fig.  19 


26 


WOODEN  BRIDGES 


80 


31.  Top  Cliords. — The  top  chord  is  usually  composed 
of  several  sticks,  as  shown  in  Fig.  20,  in  which  (a)  is  a  top 
view  and  (b)  a  side  elevation  of  a  top  chord  composed  of 
four  sticks.  The  four  sticks  are  bolted  together  by  means  of 
bolts  c ,  c,  so  they  will  act  as  a  single  member,  and  are  held  at 
the  proper  distance  apart  (usually  1  or  2  inches  for  ventilation 
to  prevent  rot)  by  means  of  oak  keys  d,  d  about  3  inches 
thick  and  12  inches  long,  set  into  the  sides  of  the  sticks.  The 
sticks  are  usually  made  about  as  long  as  it  is  possible  to  get 
them,  and  in  the  top  chord  are  spliced  at  the  centers  of  the 
keys,  as  shown  at  <?,  e  and  /,  /.  The  ends  of  the  spliced  portions 


are  cut  off  perfectly  square  and  brought  into  close  contact 
throughout  the  width  and  depth  of  the  stick.  Not  more  than 
one  stick  should  be  spliced  at  one  set  of  keys. 

32.  Bottom  Chord. — The  bottom  chord  is  composed 
of  several  sticks  bolted  together,  at  intervals  of  about  6  feet, 
in  the  same  way  as  the  top  chord.  The  difference  between 
the  two  chords  lies  in  the  method  of  splicing.  Since  the  stress 
in  the  bottom  chord  is  tension,  some  means  must  be  employed 
to  transmit  the  stress  from  one  portion  of  a  spliced  stick  to 
the  other  portion.  A  common  form  of  splice  is  shown  in 
Fig.  21,  in  which  {a)  is  a  plan  and  ( b )  an  elevation  of  a 


80 


WOODEN  BRIDGES 


27 


portion  of  a  bottom  chord,  showing  a  splice  at  c,c.  The  ends 
of  the  portions  to  be  spliced  are  cut  off  square  in  the  same 
way  as  for  the  top  chord;  oak  cleats  d,  d ,  about  6  or  7  feet 
long,  are  fitted  into  the  sides  of  the  sticks  that  are  to 


(t>J 


Fig.  21 

be  spliced,  and  the  whole  is  bolted  together  as  shown  in  the 
figure.  The  stress  is  transmitted  to  the  cleats  and  by  them 
is  transmitted  around  the  joint. 

Another  form  of  splice  is  shown  in  Fig.  22;  it  differs  from 
the  splice  shown  in  Fig.  21  principally  in  that  the  cleats  d,  d 
are  made  of  iron  or  steel  instead  of  wood. 


Fig.  22 


Fig.  23  shows  a  combination  of  parts  that  is  sometimes 
used  to  splice  the  bottom  chords  of  Howe  trusses.  In  this 
figure,  ( a )  and  {b)  are  castings  with  short  cylindrical  pro¬ 
jections  e ,  e.  Holes  are  bored  in  the  sides  of  the  members 


28 


WOODEN  BRIDGES 


§80 


to  be  spliced,  and  the  castings  placed  in  such  a  position  that 
the  projections  e ,  e  fit  exactly  into  the  bored  holes.  The 
castings  are  bolted  in  this  position.  The  cleat  /  shown 
at  ( d )  is  then  hooked  over  the  projections  g,g  on  the  cast¬ 
ings,  and  the  wedge  w,  shown  at  (e) ,  is  inserted  between 


Q=r  =r- .  __f) 

(d) 

Fig.  23 

the  end  of  the  right-hand  projection  and  the  inside  of  the 
cleat.  The  wedge  is  driven  in  so  as  to  make  the  cleat  fit 
tight  at  both  ends.  Two  cleats  are  used  in  this  case,  one 
on  each  side,  in  the  same  way  as  two  are  used  in  Figs.  21 
and  22. 

33.  Design  of  Splice. — The  splice  shown  in  Fig.  21 
may  fail  in  any  one  of  five  ways.  Referring  to  Fig.  24, 


Fig.  24 


they  are  as  follows:  (1)  by  the  breaking  of  the  cleats 
between  a  and  a'  in  tension;  (2)  by  the  shearing  of  the 
cleats  from  a  to  b  along  the  grain;  (3)  by  the  crushing  of  the 
ends  of  the  fibers  where  the  cleats  and  the  shoulders  on  the 
stick  come  together  at  ac  in  bearing  along  the  grain;  (4)  by 


§80 


WOODEN  BRIDGES 


29 


the  shearing  of  the  end  of,  the  stick  from  c  to  c’  along  the 
grain;  (5)  by  the  breaking  of  the  main  stick  where  it  is  cut 
into  the  most;  that  is,  between  c  and  d ,  in  direct  tension. 
In  a  well-designed  joint,  the  resistance  to  failure  from  each 
of  these  causes  should  be  as  nearly  as  possible  the  same,  and, 
in  designing,  the  dimensions  are  so  proportioned  that  the 
working  stresses  given  in  Art.  8  are  not  exceeded. 

34.  Case  I. — In  the  first  case  mentioned  in  the  pre¬ 
ceding  article,  the  amount  of  stress  that  can  be  transmitted 
by  the  cleats  in  tension  is  the  product  of  the  net  area  of  the 
cleats  and  the  working  stress  in  tension.  In  finding  the  net 
area  of  a  cleat,  it  is  necessary  to  deduct  from  the  gross 
section  the  area  of  the  bolt  holes.  As  a  rule,  it  is  suffi¬ 
ciently  accurate  to  take  the  net  depth  of  the  cleat  as  2  inches 
less  than  the  gross  depth.  For  example,  if  each  cleat  is 
made  of  white  oak  16  inches  deep  and  li  inches  thick,  the 
net  area  of  two  cleats  [since  the  net  depth  is  2  inches  less 
than  the  gross  depth,  Fig.  21  (b)~\  is  2  X  ( 16  —  2)  X  H  =  42 
square  inches.  The  working  stress  st  in  tension  for  white 
oak  is  given  in  Art.  8  as  900  pounds  per  square  inch;  then, 
the  amount  of  stress  that  can  be  transmitted  by  the  two 
cleats  in  tension  is  42  X  900  =  37,800  pounds. 

35.  Case  II. — In  the  second  case,  the  amount  of  stress 
that  can  be  transmitted  by  the  two  cleats  in  shearing  along 
the  grain  is  the  product  of  the  area  in  shear  and  the  allow¬ 
able  shearing  stress.  For  example,  if  each  cleat  is  made  of 
white  oak  16  inches  deep,  and  the  length  ab  (Fig.  24)  sub¬ 
jected  to  shear  is  12  inches,  the  area  subjected  to  shearing  is 
2  X  12  X  16  =  384  square  inches.  Then,  since  the  working 
stress  ss  in  shear  along  the  grain  is,  for  white  oak,  100 
pounds  per  square  inch  (Art.  8),  the  amount  of  stress  that 
can  be  transmitted  is  384  X  100  =  38,400  pounds. 

36.  Case  III. — In  the  third  case,  the  amount  of  stress 
that  can  be  transmitted  by  the  bearing  area  between  the 
cleats  and  the  shoulders  on  the  member  is  the  product  of 
the  bearing  area  and  the  working  stress  in  bearing  along  the 
grain.  For  example,  if  the  shoulders  ac  are  li  inches  wide, 


30 


WOODEN  BRIDGES 


§80 


the  depth  of  the  member  is  16  inches,  and  the  cleats  are  of 
white  oak  and  the  member  of  white  pine,  the  area  of  bearing 
is  2  X  16  X  1  i  =  48  square  inches.  The  allowable  intensity 
Sg  of  bearing  along  the  grain  of  white  oak  is  given  in  Art.  8 
as  1,250  pounds,  and  on  white  pine  as  800  pounds  per  square 
inch.  Since  the  latter  is  the  smaller,  it  must  be  used;  the  stress 
that  can  be  transmitted  is,  therefore,  48  X  800  =  38,400 
pounds. 

37.  Case  IV. — In  the  fourth  case,  the  amount  of  stress 
that  can  be  transmitted  by  the  section  cc\  Fig.  24,  of  the 
member  in  shearing  along  the  grain  is  the  product  of  the 
area  in  shear  and  the  allowable  shearing  stress.  For  exam¬ 
ple,  if  the  member  is  white  pine,  the  depth  of  the  member 
16  inches,  and  the  distance  cc'  24  inches,  the  area  in  shear  is 
2  X  16  X  24  =  768  square  inches.  Then,  since  the  working 
stress  s*  in  shear  is,  for  white  pine,  50  pounds  per  square 
inch,  the  amount  of  stress  that  can  be  transmitted  is 
768  X  50  =  38,400  pounds. 

38.  Case  V. — In  the  fifth  case,  the  amount  of  stress 
that  can  be  transmitted  by  the  member  where  it  is  cut  into 
to  admit  the  cleats  is  the  product  of  the  net  area  of  the 
decreased  portion  of  the  member  and  the  working  stress  in 
tension.  In  finding  the  net  area  of  the  stick,  it  is  customary 
to  deduct  the  area  of  the  bolt  holes  from  the  gross  section  of 
the  member.  As  a  rule,  the  bolts  are  staggered  at  this 
connection,  so  that  it  is  sufficient  to  take  the  net  depth  of 
the  stick  as  1  inch  less  than  the  gross  depth.  For  example, 
if  the  stick  is  white  pine  and  has  a  gross  width  of  7  inches, 
the  gross  depth  is  16  inches  and  the  notches  are  li  inches 
deep,  the  net  width  is  7  —  2  X  li  =  4  inches,  and  the  net 
depth  (decreased  by  one  bolt,  Fig.  21)  is  16  —  1  =  15  inches; 
then,  the  net  area  is  4  X  15  =  60  square  inches.  Since  the 
working  stress  st  in  tension  is  650  pounds  per  square  inch 
(Art.  8),  the  amount  of  stress  that  can  be  transmitted  is 
60  X  650  =  39,000  pounds. 

39.  The  dimensions  of  the  splice  that  has  been  consid¬ 
ered  in  the  examples  in  the  preceding  articles  are  shown  in 


80 


WOODEN  BRIDGES 


31 


Fig.  25.  This  form  of  splice  is  frequently  used.  The  bolts 
that  hold  together  the  various  parts  of  the  splice  should  not 
be  considered  as  transmitting  any  part  of  the  stress;  they 


Fig.  25 


serve  simply  to  hold  the  parts  so  that  they  will  work 
together. 

40.  [Lateral  System. — The  lateral  trusses  are  formed 
in  the  same  way  as  the  vertical  trusses.  The  transverse 
members  are  composed  of  rods  and  the  inclined  members  of 

t 

timber.  They  are  connected  to  the  sides  of  the  chords  by 
chord  blocks,  or  castings,  in  the  same  way  as  the  web  mem¬ 
bers  of  the  vertical  trusses  are  connected  to  the  chords. 


EXAMPLES  FOR  PRACTICE 

1.  If  the  cleats  shown  in  Fig.  24  are  of  white  oak,  14  inches  deep 

and  lj  inches  thick,  how  much  stress  can  they  transmit  without 
exceeding  the  working  stress  in  tension?  Ans.  27,000  lb. 

2.  If,  in  example  1,  the  length  of  each  cleat  subjected  to  shear  is 

12  inches,  how  much  stress  can  the  cleats  transmit  without  exceeding 
the  working  stress  in  shearing  along  the  grain?  Ans.  33,600  lb. 

3.  If  the  main  ,  member  is  of  white  pine  and  the  width  of  the 

shoulder  where  the  cleat  bears  on  the  member  is  1-j-  inches,  how  much 
stress  can  be  transmitted  without  exceeding  the  working  stress  in 
bearing  along  the  grain?^  Ans.  28,000  lb. 

4.  If  the  length  of  the  member  from  the  shoulder  to  the  end  is 
20  inches,  how  much  stress  can  be  transmitted  by  the  member  without 
exceeding  the  working  stress  in  shearing  along  the  grain? 

Ans.  28,000  lb. 

5.  If  the  thickness  of  the  member  where  it  is  cut  into  for  the  ends 

of  the  cleats  is  3g  inches,  how  much  stress  can  be  transmitted  without 
exceeding  the  working  stress  in  tension?  Ans.  29,600  lb. 


32 


WOODEN  BRIDGES 


§  80 


/ 


TOWNE  LATTICE  TRUSS 

41.  General  Description. — Fig.  26  shows  a  type  of 
truss,  called  the  Towne  lattice  truss,  that  is  used  to  some 
extent  at  the  present  time:  (a)  is  the  elevation  of  the  end 
portion  of  a  truss,  and  ( b )  is  a  cross-section  on  C  C.  In 
this  truss,  all  the  members  are  wood,  the  only  metal  being 
the  bolts  used  to  hold  the  members  together.  The  chords 
consist  of  the  horizontal  members  cc,  dd,  ee ,  and  //. 
The  two  portions  cc  and  dd  form  the  top  chord;  the  two 
portions  ee  and  //  form  the  bottom  chord.  Each  portion 
of  the  chords  is  composed  of  several  sticks,  as  shown  in 
cross-section  in  Fig.  26  ( b .)  The  web  consists  of  a  large 
number  of  flat  planks,  the  ends  of  which  are  connected  to 
each  other  and  to  the  chords.  The  horizontal  member  gg 
consists  of  two  pieces  and  serves  the  purpose  of  stiffening 
the  web  members  near  the  center  of  the  length.  The  trusses 
are  stiffened  at  the  ends  by  means  of  vertical  timbers  h  h 
and  i  i  bolted  to  the  sides  of  the  web  members.  .  The  ends 
of  the  trusses  rest  on  blocking  j  j  that  is  supported  on  the 
bridge  seats. 

42.  Floorbeams. — When  these  trusses  are  used,  the 

floorbeams  are  connected  below  the  bottom  chord  as  shown 

at  kk  in  Fig.  26.  The  bolts  /,  /  pass  through  the  lower 

portion  of  the  bottom  chord  and  through  the  ends  of  the 
* 

floorbeams.  The  latter  are  usually  spaced  from  2  to  3  feet 
apart  in  this  type  of  bridge. 

43.  Connection  of  Web  Members  to  Chords. — The 
method  of  connecting  the  web  members  to  the  chords  is 
shown  in  detail  in  Fig.  27,  in  which  a  a  and  bb  are  web 
members  and  cc  is  the  chord  member.  At  d,  the  intersection 
of  the  center  lines  of  the  members,  an  iron  bolt  about  1  inch 
in  diameter  is  driven  through  a  bored  hole,  and  tightened 
up.  Oak  pins  e,e,  commonly  called  treenails,  having  the 


Fig.  26 


34 


WOODEN  BRIDGES 


§80 


same  diameter  and  nearly  the  same  length  as  the  bolt,  are 
also  driven  through  bored  holes,  and  serve  to  transmit  the 
stresses  to  and  from  the  members.  The  amount  of  stress 


that  can  be  transmitted  to  any  of  the  members  by  the 
joint  shown  in  Fig.  27  is  usually  assumed  in  practice  to  be 
7,500  pounds. 

44.  Splices  in  Chord  Members. — The  sticks  that  form 
the  top  chord  are  joined  by  cutting  the  ends  square  and 

bringing  them  into 
good  contact  in  much 
the  same  way  as  in 
the  Howe  truss.  The 
several  sticks  that 
form  the  bottom 
chord  are  usually 
spliced  as  shown  in 
Fig.  28.  The  ends 
are  brought  together, 
and  wrought-iron  or 
steel  pieces  dy  d  are  inserted  in  holes  cut  in  the  members; 
long  U-shaped  bolts  e,  e  are  placed  over  the  ends  of  the 
pieces  d ,  d.  The  nuts  /,  /  serve  to  tighten  up  the  bolts 


§80 


WOODEN  BRIDGES 


35 


so  that  they  will  bear  firmly  against  the  top  and  bottom  of 
the  pieces  d,  d. 

45.  .Lateral  System. — The  lateral  trusses  are  usually 
made  the  same  as  for  the  Howe  truss,  and  the  members  con¬ 
nected  to  the  sides  of  the  members  by  castings  or  chord 
blocks.  In  addition,  transverse  frames  are  put  in,  as  shown 
in  Fig.  26  (b),  and  curved  knee  braces  or  brackets  m  are 
placed  between  the  bottom  of  the  transverse  frame  and  the 
web  members  of  the  truss. 

46.  Protection  of  Truss. — To  prevent  deterioration  on 
account  of  the  weather,  it  is  customary  to  shelter  this  truss, 
and  in  some  cases  Howe  trusses  also,  by  building  a  roof  and 
sides,  as  shown  in  Fig.  26  (b) .  The  roof  n  n  is  usually 
composed  of  1-inch  boards  supported  by  and  nailed  to 
joists  o,o  on  top  of  the  truss.  The  sides  p,p  also  consist  of 
1-inch  boards  that  are  nailed  to  the  pieces  q,  q  bolted  to  the 
sides  of  the  trusses. 


COMBINATION  TRUSSES 

47.  General  Description. — Although,  strictly  speak¬ 
ing,  a  combination  truss  is  any  truss  in  which  some  mem¬ 
bers  are  of  wood  and  some  of  metal,  the  name  is  generally 
restricted  to  pin-connected  trusses  in  which  the  compression 
members  are  wood  and  the  tension  members  are  steel  or 
iron.  The  Pratt  and  the  Baltimore  are  the  two  forms  of 
truss  that  are  most  used  for  this  construction.  In  all  com¬ 
bination  trusses,  the  details  of  the  connections  of  the  wooden 
members  are  arranged  in  such  a  way  that  the  members  can 
be  removed  and  replaced  without  the  necessity  of  taking 
down  the  truss.  This  arrangement  is  necessary  because  the 
wooden  members  decay  and  must  be  renewed  from  time  to 
time,  while  the  steel,  if  properly  [taken  care  of,  will  last 
almost  indefinitely. 

48.  Bottom  Chord  Joint. — Fig.  29  shows  a  bottom 
chord  joint  of  a  combination  truss:  {a)  is  the  elevation  and 
(b)  the  side  view  of  the  joint.  The  only  difference  between 


36 


WOODEN  BRIDGES 


80 


this  joint  and  that  in  a  steel  pin-connected  truss  is  in  the 
connection  of  the  vertical  member  to  the  pin.  This  is  accom- 

D 


r  \ 

EE 


Fig.  29 


plished  by  attaching-  to  the  end  of  the  member  a  casting  /, 
having  a  projection^  that  fits  into  a  groove  in  the  end  of  the, 


/ 


Fig.  30 

member.  The  casting  has  two  sides  or  webs  h  that  bear  on 
the  pin.  The  bolt  i  is  simply  for  the  purpose  of  holding  the 


§80 


WOODEN  BRIDGES 


37 


member  in  place  on  the  casting,  and  does  not  transmit  any 
stress.  The  thickness  of  metal  in  the  casting,  which  should 
always  be  a  steel  casting,  is  usually  not  less  than  1  inch. 

49.  Top  Chord  Joint. — Fig.  30  shows  a  top  chord  joint 
of  a  combination  truss:  {a)  is  the  top  view,  (b)  is  the  eleva¬ 
tion,  and  (c)  is  the  side  view  of  the  joint.  The  ends  of  the 

top  chord  members  abut  on  the  sides  of  a  casting//,  and  are 
$ 

A  A.rSi  a 


Fig.  31 

held  in  place  on  the  casting  by  means  of  bolts  g,g  that 
pass  through  the  ends  of  the  members  and  through  projec¬ 
tions  h,  h  on  the  sides  of  the  casting.  The  vertical  abuts  on 
the  under  side  of  the  casting,  and  is  held  in  place  by  a 
bolt  i  that  passes  through  a  projection  j  on  the  under  side. 
The  sides  of  the  casting  that  are  in  contact  with  the  ends  of 
the  chord  members  are  connected  by  webs  or  diaphragms  k>  k 


38 


WOODEN  BRIDGES 


§80 


about  opposite  the  centers  of  the  sticks.  These  webs  pro¬ 
vide  also  a  bearing  for  the  pin  that  passes  through  the  cast¬ 
ing  and  holds  the  ends  of  the  eyebars  in  place.  The  casting 
is  further  stiffened  by  inclined  webs  /,  /  between  the  webs  k,  k 
and  the  bearing  surfaces. 

50.  Hip  Joint. — The  detail  at  the  hip  joint  is  somewhat 
different  from  the  other  top  chord  joints.  Fig.  31  shows  a 
hip  joint:  (a)  is  the  top  view,  and  (b)  the  elevation  of  the 
joint.  The  end  post  a  B  and  the  top  chord  B  C  are  bolted  to 
separate  castings;  these  are  furnished  with  webs  or  diaphragms 
for  bearing  on  the  pin  arranged  in  such  a  way  that  the  hip 
vertical  b  B  and  the  end  diagonal  Be  can  also  connect  to  the 
pin.  In  the  figure,  the  hip  vertical  is  placed  inside  of  both 
castings,  and  the  end  diagonal  is  placed  between  the  two 
castings. 

51.  Design  of  Pins. — The  pins  in  a  combination  truss 
are  designed  in  the  same  general  manner  as  those  in  a  steel 
pin-connected  truss.  The  method  of  procedure  is  fully 
described  in  Design  of  a  Highway  Truss  Bridge ,  Part  2. 


ROOF  TRUSSES 


INTRODUCTION 


1.  Conditions  Governing  Use  of  Roof  Trusses. 
Trusses  are  frequently  employed  to  support  the  roofs  of 
buildings  in  cases  where  a  large  area  of  floor  clear  of  inter¬ 
mediate  walls  and  columns*  is  desired,  and  when  so  used  are 
called  roof  trusses.  Roof  trusses  are  usually  set  at  right 
angles  to  the  length  of  the  building,  so  as  to  make  the  span 
as  short  as  possible;  and  their  ends  either  rest  on  top  of  the 
side  walls  or  are  supported  by  columns  embedded  therein. 

2.  Types  of  Roof  Trusses. — The  same  general  types 
of  trusses  are  used  for. roofs  as  for  bridges,  except  that  the 
inclinations  of  the  chords  of  roof  trusses  are  made  to  conform 
with  the  slope  of  the  roof  and  the  required  underneath  clear¬ 
ance.  This  gives  rise  to  special  types,  some  of  which  are 
illustrated  in  Figs.  1  to  15.  The  simplest  type  of  roof  truss 
is  shown  in  Fig.  1;  it  consists  simply  of  the  two  inclined 


b 


d 

Fig.  2 


Fig.  1 


struts  a  b  and  be ,  the  lower  joints  of  which  are  connected  by 
the  horizontal  chord  or  bottom  tie  ac.  This  type  of  truss 
may  be  used  for  spans  up  to  20  feet.  In  Fig.  2,  the  long 
horizontal  chord  or  tie  ac  is  supported  at  the  center  by  the 
vertical  tie  b  d.  This  type  of  truss  may  be  used  for  spans 


COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 


§81 


ROOF  TRUSSES 


§81 


up  to  30  feet.  For  spans  from  30  to  40  feet,  the  form  shown 
in  Fig.  3  may  be  used.  In  this  truss,  the  inclined  struts  ab 

and  be  are  supported  at 
their  center  points  by 
the  inclined  struts  de 
and  df ;  the  lower  ends 
of  these  struts  are  sup¬ 
ported  by  the  vertical 
tie  b  d.  For  spans  up  to 
40  feet,  the  type  shown  in  Fig.  4  is  sometimes  used.  When 
built  of  timber,  with  the  tie  ac  continuous,  or  in  one  piece 


from  a  to  c ,  the  diagonals  in  the  center  panel  are  sometimes 
omitted.  The  types  shown  in  Figs.  5,  6,  7,  8,  and  9  are  used 


a 

Fig.  5 


for  all  spans,  the  particular  type  chosen  for  any  special  case 
depending  on  local  conditions,  and,  to  a  great  extent,  on  the 


judgment  of  the  designer.  In  Figs.  5,  6,  and  7,  the  slopes  a  b 
and  be  are  each  divided  into  a  number  of  equal  spaces.  In 
Fig.  7,  the  web  members  dd  andee  are  at  right  angles  to  the 


81 


ROOF  TRUSSES 


3 


slope.  In  Figs.,  8  and  9,  the  construction  shown  above  the 
trusses  in  dotted  lines  is  for  the  purpose  of  giving  the  sur¬ 
face  of  the  roof  an  even  slope. 


3.  All  the  trusses  considered  in  the  preceding  article  have 
horizontal  lower  chords.  It  is  often  desired  to  have  greater 
headroom,  or  clearance,  beneath  the  trusses  at  the  center  of 
the  building  than  at 
the  sides.  In  such  a 
case,  the  walls  or  col¬ 
umns  that  support 
the  ends  of  the  roof 
trusses  are  frequently 
not  carried  as  high  as  the  required  height  at  the  center  of  the 
building,  and  one  of  the  types  of  roof  trusses  shown  in 
Figs.  10  to  13  is  used. 


\ 


4  ROOF  TRUSSES  §  81 

4.  For  supporting-  the  roofs  of  station  platforms,  grand 
stands,  etc.,  the  arrangement  shown  in  Fig.  14  is  frequently 

employed.  It  con¬ 
sists  of  a  truss  resting 
on  two  columns;  the 
ends  of  the  truss  over¬ 
hang  the  supports, 
forming  cantilevers. 
In  shop  and  mill 
buildings,  in  which 
the  roof  trusses  are 
supported  on  col¬ 
umns,  the  lower  chord 
of  the  truss  is  frequently  connected  to  the  columns  by  inclined 
struts,  as  shown  at  b  in  Fig.  15;  these  struts  are  usually  pro¬ 
jections  of  one  of  the  web  members.  The  projection  at  the 
top  of  Fig.  15  is  commonly  called  a  monitor,  and  serves 
the  purpose  of  providing  vertical  skylights  at  c ,  c.  The  mem¬ 
bers  of  the  monitor 
do  not  form  part  of 
the  truss,  but  are 
simply  for  the  pur¬ 
pose  of  transmitting 
to  the  truss  any  loads 
that  may  come  on  the 
monitor. 

5.  Distance  Be¬ 
tween  Trusses. 

The  distance  between 
trusses  depends  to 
some  extent  on  the 
architectural  design; 
that  is,  the  location  of  windows,  doors,  etc.  It  is  customary, 
in  designing  a  building,  to  arrange  it  in  a  number  of  sec¬ 
tions,  or  bays,  and  to  have  the  same  openings  for  windows 
in  each  bay.  Between  the  bays,  the  wall  is  carried  up  solid 
from  the  foundation.  The  trusses  usually  rest  on  this  solid 


Fig.  14 


§81 


ROOF  TRUSSES 


5 


wall  or  on  columns  embedded  in  it.  It  is  bad  practice  to 
have  a  truss  rest  on  a  wall  directly  over  the  opening  for  a 
door  or  a  window.  There  is  usually  a  roof  truss  at  the  junc¬ 
tion  of  each  two  bays 
and  in  each  end  wall. 

It  has  been  found  in 
practice  that  it  is  well 
to  have  the  distance 
between  trusses  about 
one -fourth  the  span. 

They  are  seldom 
placed  less  than  10 
feet  and  never  more 
than  about  50  feet 
center  to  center. 

6.  Span  and  1=5  Fig  15 

Rise. — The  horizontal  distance  /,  Fig.  16,  between  the  sup¬ 
ports  of  a  roof  truss  is  called  the  span.  The  vertical  dis¬ 
tance  r  from  the  top  of  the  truss  to  the  level  of  the  supports 
is  called  the  rise.  The  vertical  distance  h  from  the  inter¬ 
sections  of  the  inclined  top  members  to  the  center  of  the  lower 

chord  at  the  center  of 
the  span  is  called  the 
depth  of  the  truss. 
In  some  cases,  h  is 
made  equal  to  r,  in 
others  h  is  made  less 


2,  3,  5,  6,  7,  are  called  main  rafters,  or  simply  rafters. 
The  lower  chord  or  member  ac  is  called  simply  the  chord. 

The  trusses  are  connected  to  each  other  at  the  joints  of  the 
rafters  by  beams  called  purlins,  as  shown  in  cross-section 


6 


ROOF  TRUSSES 


§81 


in  Fig.  17  (a).  When  the  distance  between  trusses  is  small, 
channels  or  I  beams  are  used  for  purlins;  when  the  distance 
between  trusses  is  greater  than  20  or  25  feet,  riveted  girders 
or  trusses  are  used.  The  ends  of  the  purlins  sometimes  rest 
on  top  of  the  rafters,  as  shown  in  Fig.  17  ( a ),  and  are  some¬ 
times  connected  to  the  web  members,  as  shown  in  Fig.  17  ( b ). 


Fig.  17 

As  the  surface  of  the  roof  is  not  horizontal,  there  is  a  tend¬ 
ency  for  the  purlins  to  sag  or  deflect  sidewise.  To  counter¬ 
act  this  tendency,  the  purlins  are  connected  at  one  or  more 
points  intermediate  between  the  trusses  by  means  of  tie-rods 
c ,  Fig.  17  ( a ),  that  run  from  the  purlin  at  the  top,  or  ridge, 
down  both  sides  of  the  roof. 

8.  On  top  of  the  purlins,  and  at  right  angles  to  them,  are 
smaller  beams  d ,  Fig.  17  (a) ,  close  together.  They  are  called 
common  rafters,  and  are  usually  spaced  about  2  feet  apart. 
They  support  the  roofing  material  and  covering,  and  transmit 
any  load  on  the  roof  to  the  purlins.  The  purlins  transmit  the 
load  to  the  trusses  at  the  joints  of  the  main  rafter. 

9.  Panel  Length. — The  panel  length  of  a  roof  truss 
is  the  distance  between  two  successive  joints  of  the  rafter, 
measured  along  the  slope.  It  may  be  found  by  the  formula 

,  V/’  +  4  r' 

P  = - 

n 

in  which  p  is  the  panel  length  and  n  is  the  number  of  panels. 


§81 


ROOF  TRUSSES 


7 


10.  Slope  of  Roof. — The  slope  of  the  roof  is  frequently 
spoken  of  in  terms  of  the  ratio  between  the  rise  and  the  span. 
This  ratio  is  called  the  pitch.  Thus,  a  pitch  of  i  means  that 
the  rise  of  the  roof  is  i  of  the  span.  The  slope  is  also  spoken 
of  as  the  ratio  of  the  vertical  distance,  called  the  rise,  to  the 
corresponding-  horizontal  distance,  called  the  run;  thus,  1  of 
rise  to  2  of  run  means  that  for  every  2  feet  measured  hori¬ 
zontally,  the  roof  rises  1  foot  vertically.  This  ratio  is  usually 
spoken  of  as  1  in  2,  1  in  3,  etc.  This  form  will  be  used  in 
the  following  articles. 

11.  Roof  Covering. — The  materials  commonly  used 
for  roof  coverings  are  shingles,  slate,  tile,  copper,  tin,  corru¬ 
gated  iron,  felt,  asphalt,  tar,  and  gravel.  Thin  slabs  of  rein” 
forced  concrete  have  also  been  used  in  a  number  of  cases. 
With  all  of  these  materials,  except  the  reinforced-concrete 
slab,  it  is  customary  to  put  wooden  sheathing  about  1  inch 

thick  directly  on  top  of  the  common  rafters,  so  as  to  afford 
$ 

the  roofing  material  a  flat  surface  on  which  to  rest.  Shingles 
and  tile  may  be  used  on  all  slopes  greater  than  1  in  2,  and 
slate  and  corrugated  iron  on  all  slopes  greater  than  1  in  3. 
Copper  and  tin  with  the  joints  well  soldered,  and  also  rein¬ 
forced  concrete,  may  be  used  on  all  slopes.  Felt,  with 
asphalt  or  tar  and  gravel,  is  used  on  flat  roofs  having  slopes 
less  than  1  in  4.  If  used  on  greater  slopes,  the  tar  or  asphalt 
will  run  down  when  it  gets  warm,  and  leave  the  upper  part 
of  the  roof  exposed.  The  kind  of  roof  covering  adopted 
depends  mainly,  on  the  type  of  building  and  on  the  amount 
of  money  available. 


8 


ROOF  TRUSSES 


81 


LOADS  AND  STRESSES 

12.  Loads. — The  loads  that  must  be  supported  by  roof 
trusses  are  the  dead  load,  which  consists  of  the  weight  of 
roof  covering,  rafters,  purlins,  and  trusses;  the  live  load, 
which  consists  of  the  heaviest  snowfall;  and  the  wind  load, 
which  is  due  to  the  pressure  of  the  wind.  In  addition,  if 
ceilings  or  balconies  are  attached  to  the  chords  of  the 
trusses,  the  latter  must  be  designed  to  support  them. 

13.  Lead  Load. — The  dead  load  depends  on  the  kind 
of  roof  covering  used,  the  distance  between  rafters  and 
purlins,  and  the  distance  between  trusses  and  supports.  The; 
approximate  weights  of  the  usual  roof  coverings  and  ceiling 


are  as  follows: 

Pounds 

Materials  per  Square 

Foot 

Shingles .  2 

Slate .  8 

Corrugated  tile .  9 

Tile  on  3-inch  fireproof  blocks  . 35 

Copper  and  tin  .  \\ 

Corrugated  iron .  2 

Felt  with  tar  or  asphalt  and  gravel .  9 

Wooden  sheathing  1  inch  thick .  4 

Lath-and-plaster  ceiling  . 10 

Glass  skylight,  including  frames  .  8 

Concrete  slab,  including  reinforcement  (per 
inch  of  thickness)  . . 12 


The  weight  of  the  common  rafters,  purlins,  and  trusses 
should  first  be  assumed,  and  the  weights  revised  after  the 
members  have  been  designed.  If  balconies  are  attached  to 
the  trusses,  their  weight  must  be  calculated. 

14.  Snow  Load. — The  weight  of  snow  that  may  fall  and 
remain  on  a  roof  in  winter  depends  on  the  slope  of  the  roof 


§81 


ROOF  TRUSSES 


0 


and  on  the  climate.  It  is  customary  to  assume  a  weight  of 
30  pounds  per  square  foot  in  the  northern  part  of  the  United 
States,  and  10  pounds  per  square  foot  in  the  southern  part, 
on  roofs  the  slope  of  which  is  not  greater  than  1  in  2.  These 
loads  are  gradually  decreased  for  steeper  roofs,  up  to  a  slope 
of  2  in  1,  for  which  the  snow  load  is  neglected,  it  being 
assumed  that  the  snow  will  slide  off  by  its  own  weight. 


15.  Wind  Pressure. — In  considering  the  pressure  of 
the  wind  on  a  roof,  it  is  customary  to  resolve  it  into  two 
components,  one  parallel  with  the  surface  of  the  roof,  arid 
the  other  normal  to  that  surface.  In  calculating  the  stresses 
due  to  the  wind  pressure,  the  former  component  is  neglected. 
The  intensity  of  the  normal  component  varies  with  the  slope, 
being  greater  for  steep  than  for  flat  roofs.  The  normal 
intensities  of  wind  pressure  per  square  foot  on  roofs  of  dif¬ 
ferent  slopes  are  usually  taken  as  follows: 


Normal 

Slope  of  Roof 

Pounds  per 
Square  Foot 

Flat  roof .  0  , 

1  in  5  (tV  pitch) . 10 

1  in  2i  (i  pitch) . 20 

1  in  2  (i  pitch) . 25 

1  in  lv  (i  pitch) . 30 

1  in  1  (|  pitch)  .  .  .  . . 36 

1  in  I,  and  steeper . 40 

Since  wind  can  blow  in  but  one  direction  at  any  one  time, 
it  is  customary  to  consider  but  one  side  of  a  roof  truss 
loaded  with  wind  load  at  any  one  time. 


16.  Panel  Loads. — Each  truss,  except  those  at  the 
ends  of  the  building,  is  assumed  to  support  one-half  of  the 
load  in  each  of  the  two  adjacent  bays.  If  the  lengths  b  of 
the  bays  are  all  equal,  and  the  panel  lengths  p  of  the  rafter 
are  equal,  and  the  load  per  square  foot  of  roof  surface  for 
any  loading  is  w ,  the  panel  load  W  for  that  loading  is  given 
by  the  formula 

W  =  w  bp 


10 


ROOF  TRUSSES 


81 


For  dead  and  snow  loads,  the  panel  loads  are  vertical,  and 
the  stresses  in  the  members  are  greatest  when  there  is  a 
full  panel  load  at  each  of  the  joints  of  the  rafter,  except 

at  the  supports,  where 
the  panel  loads  will 
W_ 

2  ’ 

Fig.  18.  For  wind 
loads,  the  panel  loads 
are  inclined  and  con¬ 
sidered  normal  to  the  roof.  The  stresses  caused  in  the  mem¬ 
bers  by  the  wind  load  are  greatest  when  there  is  a  full  panel 
load  at  each  joint  of 
the  rafter  on  one-half 
of  the  truss,  except  at 
the  top  and  bottom 
joints,  where  the 

loads  will  be  as  Plo.  19 


Fig.  18 


shown  in  Fig.  19.  The  panel  loads  on  the  trusses  at  the  ends 
of  the  building  are,  as  a  rule,  one-half  those  on  the  other 
trusses. 


17.  The  panel  loads  on  the  sloping  parts  of  the  roof 
and  monitor  shown  in  Fig.  20  are  found  in  the  same  way  as 
for  other  trusses.  When  the  length  of  the  sloping  part 
of  the  roof  of  the  monitor  is  equal  to  a  panel  length  of  the 

W' 

truss,  the  panel  loads  — -  on  the  roof  of  the  monitor  are 

A 


equal  to  the  half  panel  loads  -—-  on  the  truss.  In  addition, 

A 

W" 

there  are  horizontal  wind  forces  of  — — -  at  the  top  and  bottom 

A 


of  the  vertical  side  of  the  monitor,  W"  being  the  total  wind 
pressure  on  one  bay  of  the  vertical  side,  computed  for  a 
wind  pressure  of  40  pounds  per  square  foot. 


18.  If  the  side  walls  of  the  building  are  of  masonry,  the 
wind  pressure  on  them  need  not  be  considered  in  the  design 


81 


ROOF  TRUSSES 


11 


of  the  roof  trusses.  If  the  sides  are  exposed  to  the  action  of 
the  wind,  and  are  of  wood,  corrugated  iron,  or  other  build¬ 
ing  material  attached  to  the  outside  of  the  columns,  the  wind 
pressure  on  the  side 
of  the  building  causes 
stresses  in  the  roof 
trusses,  and  hence 
must  be  taken  into 
account.  It  will  be 
assumed  that  the 
wind  pressure  on  the 
side  of  the  building 
for  a  length  of  one 
bay  is  IV"',  and  that 
one-half  of  this  is 
transmitted  to  the 

w" 

bottom  and  one -half  2“ 
to  the  top  of  the 


Fig.  20 


column,  giving  a  concentrated  load 


at  each  of  these 


points,  as  shown  in  Fig.  20. 


19.  Reactions. — The  reactions  due  to  the  dead  and 
snow  loads  are  vertical,  and  are  found  in  the  same  way  as 
for  a  simple  beam.  The  reactions  due  to  the  wind  load  may 


be  vertical  or  inclined,  according  to  the  manner  in  which  the 
ends  of  the  trusses  are  connected  to  the  supports.  When  the 
ends  of  the  trusses  rest  on  top  of  the  walls,  and  both  ends 
are  anchored  down,  as  is  usual  with  spans  less  than  about 


12 


ROOF  TRUSSES 


§  si 


70  feet  long,  it  is  customary  to  assume  that  both  reactions 
are  parallel  to  the  direction  of  the  wind  panel  loads,  as 


shown  in  Fig.  21.  The  magnitude  of  the  reactions  Rx  and 
Rt  can  be  found  by  resolving  the  resultant  F  of  the  wind 


ROOF  TRUSSES 


13 


§  81 

panel  loads  into  two  components  passing  through  the  points 
of  support  and  parallel  to  the  resultant. 

20.  For  longer  spans,  it  is  customary  to  place  rollers 
under  one  end  to  provide  for  changes  in  length  due  to 
changes  in  temperature.  Since  the  truss  is  free  to  move 
horizontally  at  the  expansion  end,  no  horizontal  force  can 
be  transmitted  to  the  abutment  or  support  at  that  end, 
except  the  friction  of  the  rollers,  which  is  usually  neglected. 
All  the  horizontal  components  of  the  inclined  wind  panel 
loads  are  then  assumed  to  be  transmitted  to  the  support  at 
the  fixed  end.  The  directions  of  the  reactions  when  the  wind 
is  blowing  on  the  expansion  end  of  the  truss  are  shown  in 
Fig.  22.  The  directions  of  the  reactions  when  the  wind  is 
blowing  on  the  fixed  end  of  the  truss  are  shown  in  Fig.  23. 
In  each  of  these  figures  the  circle  at  the  left-hand  end  repre¬ 
sents  the  rollers  under  that  end  of  the  truss,  at  which  end 
the  reaction  is  vertical. 

21.  In  the  case  represented  in  Fig.  24,  it  is  customary 
to  find  the  horizontal  and  vertical  components  of  the  reac¬ 


tions  separately.  For  this  purpose,  the  various  wind  forces 
are  resolved  into  their  vertical  and  horizontal  components. 
The  vertical  components  of  the  reactions  at  C  and  C  are 
then  found  by  taking  moments  about  C'  and  C,  respectively. 
The  horizontal  components  of  the  reactions  are  found  on 

135—25 


14 


.ROOF  TRUSSES 


81 


*  '  ■  «  ■  ■ 

the  assumption  that  one-half  the  sum  of  the  horizontal  com¬ 
ponents  of  the  wind  forces  goes  to  each  support. 

If  the  columns  are  fixed  in  direction  at  the  bottom,  as  is 
usually  the  case,  points  of  inflection  may  be  taken  half  way 
between  the  lower  ends  of  the  inclined  braces  and  the  bases 
of  the  columns,  the  same  as  in  the  case  of  the  end  post  of  a 
through  truss  bridge. 

% 

22.  Method  of  Calculation. — The  stresses  in  the  mem¬ 
bers  of  roof  trusses  can  be  found  by  either  the  analytic  or  the 
graphic  method.  The  members  of  most  roof  trusses  have  so 
many  different  inclinations,  however,  that  the  work  required 
by  the  analytic  method  is  comparatively  great;  so  this  method 
is  seldom  used  in  practice.  The  graphic  method  is  especially 
useful  for  this  purpose.  The  stresses  should  be  found  sep¬ 
arately  for  the  vertical  and  for  the  inclined  loads.  When 
one  end  of  the  truss  rests  on  rollers,  the  stresses  due  to  the 
wind  should  be  found  separately  for  the  wind  blowing  in 
each  direction.  In  the  latter  case,  there  are  three  conditions 
of  loading  for  which  the  stresses  in  the  members  must  be 
found;  namely,  (1)  full  snow  load  together  with  the  dead 
load;  (2)  wind  pressure  on  the  expansion  end;  (3)  wind 
pressure  on  the  fixed  end.  The  stresses  found  in  (1)  must 
be  combined  with  those  found  in  (2)  or  (3)  to  obtain  the 
greatest  stress  in  each  member.  In  some  trusses,  there  are 
members  in  which  the  stress  is  tension  when  the  wind  acts 
on  one  side,  and  compression  when  it  acts  on  the  other. 

The  methods  of  calculation  will  now  be  illustrated  by  prac¬ 
tical  examples. 


FIRST  ILLUSTRATIVE  EXAMPLE 

23.  Data. — The  first  illustrative  example  will  be  the 
truss  shown  in  Fig.  16  (a) ,  the  data  for  which  will  be  assumed 


as  follows: 

Distance  between  trusses . b  —  15  feet 

Span . /  =  60  feet 

Rise  .  . . r  =  15  feet 

Number  of  panels . n  —  8 


§81 


ROOF  TRUSSES 


15 


Roofing  material  .  Slate  on  1-inch  wooden  sheathing 
Dead  load  of  rafters,  purlins, 

and  trusses  ....  10  pounds  per  square  foot 

Snow  load . 30  pounds  per  square  foot 

Supports  .  .  Truss  anchored  to  the  tops  of  the  walls 

at  both  ends 


24.  Panel  Length. — The  panel  length  p  is  found  by 
the  formula  in  Art.  9.  Since  /  —  60  feet,  r  —  15  feet,  and 
n  =  8,  the  formula  gives  y 


^60*  +  4  x  15* 

8 


=  8.385  feet 


25.  Panel  Loads. — The  panel  load  W  for  any  loading  is 
found  by  the  formula  in  Art.  16.  In  the  present  case, 
b  —  15  feet  and  p  =  8.385  feet. 

1.  Dead  Panel  Load . — The  dead  panel  load  consists  of  the 
weight  of  the  slate,  the  sheathing,  and  the  rafters,  purlins, 
and  trusses.  The  weight  of  the  slate  is  given  in  Art.  13  as 
8  pounds  per  square  foot,  and  the  weight  of  the  sheathing  as 
4  pounds  per  square  foot.  The  weight  of  the  rafters,  pur¬ 
lins,  and  trusses  is  given  in  the  data  as  10  pounds  per  square 
foot.  Then,  the  total  dead  load  w  is  8  +  4  +  10  =  22  pounds 
per  square  foot,  and  for  the  dead  panel  load  Wd  we  have 

Wd  =  22  X.  15  X  8.385  =  2,767  pounds 

There  will  be  seven  full  panel  loads  on  the  truss,  and,  in 
addition,  two  half  panel  loads  over  the  supports.  Since  the 
latter  loads  do  not  cause  any  stresses  in  the  members  of  the 
truss,  they  will  not  be  considered  here. 

2.  Snow  Panel  Load. — The  snow  load  is  30  pounds  per 
square  fool.  Then,  for  the  snow  panel  load  Ws,  we  have 

Ws  =  30  X  15  X  8.385  -  3,773  pounds 

3.  Wind  Pa7iel  Load. — Since  the  rise  is  15  feet  and  the 
span  is  60  feet,  the  roof  has  a  pitch  of  i,  or  a  slope  of  1  in  2. 
In  Art.  15,  the  normal  pressure  of  the  wind  on  a  roof  having 
a  slope  of  1  in  2  is  given  as  25  pounds  per  square  foot. 
Then,  denoting  the  wind  panel  load  by  Ww, 

Wio  —  25  X  15  X  8.385  =  3,144  pounds 


16 


ROOF  TRUSSES 


§81 


There  will  be  three  full  wind  panel  loads,  and,  in  addition, 
the  two  half  panel  loads  at  the  bottom  and  top,  respectively. 
Since  the  wind  panel  loads  are  inclined,  it  is  well  to  consider 
the  panel  load  over  the  support. 


26.  Stresses  Due  to  Dead  and  Snow  Loads. — In  this 
example,  it  is  best  to  consider  the  reactions  and  stresses  due 
to  the  vertical  loads  (combined  dead  and  snow  loads)  sepa¬ 
rately  from  those  due  to  the  inclined  loads  (wind  pressure). 
The  dead  panel  load  was  found  in  Art.  25  to  be  2,767  pounds; 
and  the  snow  panel  load,  3,773  pounds.  Then,  the  total  ver¬ 
tical  panel  load  is  2,767  +  3,773  =  6,540  pounds.  There  are 
seven  full  panel  loads,  as  shown  in  Fig.  25  {a).  Since  the 
loading  is  symmetrical,  the  reactions  are  equal,  and  each  is 

Z-  X  6,540  __  22,890  pounds.  The  stress  diagram  for  this 


loading  is  shown  in  Fig.  25  (b) . 

The  panel  loads  are  laid  off  on  the  line  0-7 ,  and,  since  the 
reactions  are  equal,  the  point  8  is  located  half  way  between 
0  and  7.  The  remainder  of  the  diagram  is  constructed,  as 
usual,  by  drawing  vectors  in  the  stress  diagram  parallel  to 
the  members  in  the  truss. 

It  has  been  explained  in  Graphic  Statics  that,  in  construct¬ 
ing  the  stress  diagram  for  a  truss,  it  is  necessary  to  consider, 
one  after  another,  the  joints  at  which  but  two  of  the  stresses 
are  unknown.  In  the  truss  under  consideration,  if  the  dia¬ 
gram  is  started  for  the  joint  a ,  it  will  be  found  possible  to  con¬ 
struct  it  also  for  the  joints  b  and  B.  At  each  of  the  joints  c 
and  C  there  will  then  be  three  members  in  which  the  stresses 
are  unknown,  and  the  stress  diagram  cannot  be  drawn 
directly.  In  this  case,  it  is  customary  to  consider  the  next 
joint  d  on  the  rafter,  and  to  assume,  temporarily,  the  stress 
in  one  of  the  rafter  members.  This  assumed  stress  is  only 
an  auxiliary  quantity  used  for  the  purposes  of  calculation. 
It  is  known  that  the  point  13  in  the  stress  diagram  will  lie 
on  a  line  2-13"  through  2  parallel  to  the  member  cd,  and 
that  the  point  15  lies  in  a  line  through  8  parallel  to  C  C. 
The  stress  in  cd  will  be  temporarily  assumed  equal  to  13'-2t 


§81 


ROOF  TRUSSES 


17 


and  the  polygon  13' -2-3-14' -13'  drawn  for  the  joint  d.  The 
polygon  13' -14' —15' —12' -13'  is  then  drawn  for  the  joint  D. 
This  locates  the  point  12' .  The  stress  in  c  C,  however,  will 
be  represented  by  a  vector  through  the  point  11  parallel 


to  c  C,  and  point  12  must  lie  on  this  line.  The  actual  location 
of  point  12  is  then  found  by  drawing  the  line  12'-12,  parallel 
to  13' -2  and  3-14',  to  its  intersection  with  11-12",  the  latter 


18 


ROOF  TRUSSES 


§81 


line  being  parallel  to  c  C.  This  gives  the  stress  in  c  C  {11-12) 
and  makes  it  possible  to  complete  the  stress  diagram  without 
difficulty. 

When  the  loading  is  symmetrical,  the  stress  diagram  is 
sometimes  drawn  for  only  one-half  of  the  truss,  but  it  is 
well,  as  in  the  present  case,  to  draw  the  entire  diagram  for 
a  check.  The  stresses  in  the  members  on  one  side  of  the 

center,  as  scaled  from  the  stress  diagram,  are  as  follows,  using 

/ 

the  plus  sign  for  compression  and  the  minus  sign  for  tension: 


Member 

Vector 

Stress 

(Pounds) 

a  b 

0-  9 

4-  51,200 

be 

1-10 

+  48,300 

cd 

2-13 

+  45,300 

d  e 

3-14 

+  42,400 

a  B 

8-  9 

-  45,800 

BC 

8-11 

-  39,200 

CO 

8-15 

-  26,200 

bB  , 

9-10 

+  5,800 

Be 

10-11 

-  6,500 

c  C 

11-12 

+  11,700 

cD 

12-13 

-  6,500 

dD 

13-14 

+  5,800 

CD 

12-15 

-  13,100 

De 

14-15 

-  19,600 

27.  Stresses  Due  to  Wind  Toad. — The  wind  panel 
load  was  found  in  Art.  25  to  be  3,144  pounds.  The  load¬ 
ing  on  the  truss  is  shown  in  Fig.  26  {a).  Since  the  loading  is 
inclined  and  unsymmetrical,  the  reactions  can  be  found  by 
the  graphic  method  with  much  less  work  than  by  the  analytic 
method.  For  convenience  of  reference,  the  same  notation  is 
used  as  in  Fig.  25;  the  forces  4-5,  5-5,  and  6-7  may  be  taken 
as  zero.  The  loads  are  laid  off  on  the  line  8'-4,  Fig.  26  (6), 
the  pole  P  is  chosen,  and  the  rays  P-8 '  and  P-4  are  drawn. 
The  resultant  of  all  the  wind  panel  loads  is  equal  to  8'-4 , 
and  acts  through  the  center  of  the  left-hand  side  of  the 
rafter;  that  is,  through  the  joint  c,  and  in  the  direction  eg. 


19 


20 


ROOF  TRUSSES 


§Sl 


The  funicular  gfhg  is  drawn,  and  the  reactions  4-8  and 

8-8'  are  found  by  drawing  the  ray  P-8  parallel  to  the  closing 
line  ./ h.  The  remainder  of  the  work  consists  simply  in 
drawing  the  stress  diagram  shown  in  Fig.  26  {b) .  The 
points  16,  17,  18,  19,  20,  and  21  are  not  shown  in  the  stress 
diagram,  since  they  coincide  with  15.  This  indicates  that  for 
this  loading  there  are  no  stresses  in  the  web  members  to  the 
right  of  15.  The  wind  stresses  in  the  members,  as  scaled 
from  the  stress  diagram,  are  as  follows: 

Member  Vector 


Stress 

(Pounds) 


a  b,  bc,c  d,de 
a  B 
BC 

CC ,  C'B/B'a’ 
b  B,d  D 
B  c,c  D 
cC 
CD 
De 

e  d',  df  c ',  c'  b' ,  b'  a ' 

eD',  D'  C',  d'D',D'c',\ 
c'  C',c'B',b'  B'  ) 


0-9 ,  1-10 ,  2-13,  3-14 
8-9 
8-11 
8-15 

9- 10,  13-14 

10- 11,  12-13 
11-12 
12-15 
14-15 
4-15 


+  14,100 

-  15,800 

-  12,300 
*  -  5,300 

+  3,100 

-  3,500 
+  6,300 

-  7,000 

-  10,500 
+  7,900 

0 


28.  Total  or  Combined  Stresses. — The  maximum 
total  stresses  in  the  members  are  found  by  combining  the 
stresses  due  to  the  vertical  loads  with  those  due  to  the 
inclined  loads.  The  total  combined  stresses  are: 


Member 

Stress 

(Pounds) 

Member 

Stress 

(Pounds) 

a  b 

+  65,300 

bB 

+  8,900 

be 

+  62,400 

Be 

-  10,000 

c  d 

+  59,400 

eC 

+  18,000 

d  e 

+  56,500 

eD 

-  10,000 

a  B 

-  61,600 

dD 

+  8,900 

BC 

-  51,500 

CD 

-  20,100 

CC 

-  31,500 

De 

-  30,100 

It  is  not  necessary  to  find  the  stresses  in  the  members  on 
the  right-hand  side  of  the  center,  as  they  are  the  same  as 
those  in  the  corresponding  members  on  the  left-hand  side. 


21 


ROOF  TRUSSES 


SECOND  ILLUSTRATIVE  EXAMPLE 

29.  Data. — The  second  illustrative  example  will  be  of 
the  same  general  type  as  the  truss  shown  in  Fig.  5.  The 
data  will  be  assumed  as  follows: 

Distance  between  trusses  . b  =  22  feet 

Span . I  =  100  feet 

Rise . r  —  20  feet 

Number  of  panels . n  —  10 

Roofing  material  .  .  Corrugated  iron,  no  sheathing 
Dead  load  of  rafters, 

purlins,  and  trusses  .  20  pounds  per  square  foot 

Snow  load . 25  pounds  per  square  foot 

Supports  ....  Rollers  at  left  end;  right  end  fixed 
The  outline  of  the  truss  is  shown  in  Fig.  27. 


30.  Panel  Length. — Since  l  —  100  feet,  r  —  20  feet, 
and  n  =  10,  the  formula  of  Art.  9  gives 


VlOO’  +Vx~20* 

10 


10.77  feet 


31.  Panel  Loads. — The  panel  load  W  for  any  loading 
is  given  by  the  formula  in  Art.  16.  In  the  present  case, 
b  —  22  feet  and  p  —  10.77  feet. 

1.  Dead  Panel  Load. — The  dead  load  consists  of  the  weight 
of  the  corrugated  iron,  and  the  rafters,  purlins,  and  trusses. 
The  weight  of  the  corrugated  iron  is  given  in  Art.  13  as 
2  pounds  per  square  foot.  The  weight  of  the  rafters,  purlins, 
and  trusses  is  given  in  the  data  as  20  pounds  per  square  foot. 
Then,  the  total  dead  load  is  2  +  20  =  22  pounds  per  square 
foot,  and  for  the  dead  panel  load  Wd  we  have 

I Vd  —  22  X  22  X  10.77  =  5,213  pounds 
There  will  be  nine  full  panel  loads,  and,  in  addition,  two 
half  panel  loads  over  the  supports.  Since  the  latter  loads 


22  ROOF  TRUSSES  §81 

do  not  cause  any  stresses  in  the  members  of  the  truss,  they 
will  not  be  considered. 

2.  Snow  Panel  Load. — The  snow  load  is  25  pounds  per 
square  foot  (Art.  29).  Then,  for  the  snow  panel  load  Ws 
we  have 

Ws  =  25  X  22  X  10.77  =  5,923  pounds 


3.  Wind  Panel  Load. — Since  the  rise  is  20  feet  and  the 
span  is  100  feet,  the  roof  has  a  i  pitch  or  a  slope  of  1  in  2^. 
In  Art.  15,  the  normal  pressure  of  the  wind  on  a  roof  having 


§  81  ROOF  TRUSSES  23 


a  slope  of  1  in  2i  is  given  as  20  pounds  per  square  foot. 
Then,  for  the  wind  panel  load  Ww  we  have 

Ww  =  20  X  22  X  10.77  =  4,739  pounds 
There  will  be  four  full  wind  panel  loads,  and,  in  addition, 
the  two  half  panel  loads  at  the  bottom  and  top,  respectively. 
Since  the  wind  panel  loads  are  inclined,  the  load  over  the 
support  may  cause  stresses  in  the  members  of  the  truss,  and 
it  must  be  considered. 


32.  Stresses  Due  to  Dead  and  Snow  Loads.— -In 
this  example,  it  is  best  to  consider  the  reactions  and  stresses 
due  to  the  vertical  loads  (combined  dead  and  snow  loads) 
separately  from  those  due  to  the  inclined  loads  (wind  pres¬ 
sure).  The  dead  panel  load  was  found  in  Art.  31  to  be 
5,213  pounds;  and  the  snow  panel  load,  5,923  pounds.  Then, 
the  total  vertical  panel  load  is  5,213  +  5,923  =  11,136  pounds. 
There  are  nine  full  panel  loads,  as  shown  in  Fig.  28  (a). 


Since  the  loading  is  symmetrical,  each  reaction  is 


9  X  11,136 
2 


=  50,112  pounds.  The  stress  diagram  for  this  loading  is 
shown  in  Fig.  28  (b) .  The  panel  loads  are  laid  off  on  the 
line  0-9,  and,  since  the  reactions  are  equal,  the  point  10  is 
located  half  way  between  0  and  9.  The  remainder  of  the 
diagram  is  drawn  as  usual,  presenting  no  special  difficulty. 
This  diagram  is  symmetrical  about  the  line  10-28 ,  so  that  it 
is  necessary  to  draw  but  one-half.  For  a  check,  however, 
it  is  always  advisable  to  draw  the  complete  diagram.  The 
stresses  in  the  members  on  one  side  of  the  center,  as  scaled 
from  the  stress  diagram,  are  as  follows: 


Member 

Vector 

Stress 

(Pounds) 

a  b 

0-11 

+  134,900 

be 

1-12 

+  134,900 

cd 

2-14 

+  119,900 

de 

3-16 

+  104,900 

cf 

4-18 

+  90,000 

a  B 

10-11 

-  125,300 

BC 

10-13 

-  111,400 

CD 

10-15 

-  97,400 

24  ROOF  TRUSSES  §81 


Member 

Vector 

Stress 

(Pounds) 

DE 

10-17 

-  83,500 

EE 

10-19 

-  69,600 

bB  . 

11-12 

+  11,100 

Be 

12-13 

-  17,800 

cC 

13-14 

+  16,700 

Cd 

14-15 

-  21,700 

dD 

15-16 

+  22,300 

De 

16-17 

-  26,300 

eE 

17-18 

+  27,800 

Ef 

18-19 

-  31,100 

-  IF 

19-20 

0 

33.  Stresses  Due  to  Wind  Toad. — As  it  is  stated 
in  the  data  that  one  end  of  the  truss  rests  on  rollers,  it  is 
necessary  to  find  the  stresses  both  when  the  wind  blows 
on  the  expansion  end  and  when  the  wind  blows  on  the 
fixed  end.  The  wind  panel  load  was  given  in  Art.  31  as 
4,739  pounds. 

1.  Wind  on  Expa?ision  End. — The  loading  when  the  wind 
blows  on  the  expansion  end  is  shown  in  Fig.  29  («).  The 
reaction  at  the  left  end  is  vertical;  that  at  the  right  end  is 
inclined,  and  its  direction  is  found  by  resolving  the  result¬ 
ant  A  of  the  wind  panel  loads  into  two  components,  one  ver¬ 
tical  and  passing  through  a ,  and  the  other  inclined  and 
passing  through  a'.  A  vertical  line  through  a  intersects  the 
resultant  of  the  wind  panel  loads  at  g,  a'nd  the  line  ga' 
gives  the  line  of  action  of  the  reaction  at  a'.  The  wind  panel 
loads  are  laid  off  on  the  line  10'-5 ,  Fig.  29  (b) .  The  magni¬ 
tudes  of  the  reactions  are  found  by  drawing  a  vertical  line 
through  10f  to  its  intersection  with  a  line  through  5  parallel 
to  a'g.  The  stresses  in  the  members  are  found  by  com¬ 
pleting  the  stress  diagram  in  the  usual  way.  Since  the  dia¬ 
gram  is  unsymmetrical,  it  is  necessary  to  draw  it  complete. 
The  stresses  are  as  follows: 


i 


25 


Fig.  29 


26 


ROOF  TRUSSES 


§81 


Member 

Vector 

Stress 

(Pounds) 

a  b 

0-11 

+  36,100 

be 

1-12 

+  38,000 

c  d 

2-14 

+  33,100 

de 

3-16 

+  28,100 

e  f 

4-18 

+  23,100 

a  B 

10-11 

-  32,700 

BC 

10-13 

-  26,300 

CD 

10-15 

-  19,900 

DE 

10-17 

-  13,500 

EF,FE',E'D'A 
D'  C’,  OB',  B'a'J 

10-19 

-  7,200 

bB 

11-12 

+  5,100 

Be 

12-13 

-  8,200 

cC 

13-14 

+  7,700 

Cd 

14-15 

-  10,000 

dD 

15-16 

+  10,200 

De 

16-17 

-  12,000 

e  E 

17-18 

+  12,800 

Ef 

18-19 

-  14,300 

if  F,  fE',  E'e',  e'  D', 
D' d ',  d'C',  C'c', 

\  d  B',  B'  b' 


fe ',  ef  d,  d'  d,  d  b',  b'  a'  5-19  +  17,200 

2.  Wind  oil  Fixed  End . — The  loading  when  the  wind  blows 
on  the  fixed  end  is  shown  in  Fig.  30  (a).  The  reaction 
at  the  left  end  is  vertical;  that  at  the  right  end  is  inclined, 
and  its  direction  is  found  by  resolving  the  resultant  F  of  the 
wind  panel  loads  into  two  components,  one  vertical  and 
passing  through  a,  and  the  other  inclined  and  passing 
through  a '.  A  vertical  line  through  a  intersects  the  resultant 
of  the  wind  panel  loads  at  g,  and  the  line  g  a’  gives  the 
direction  of  the  reaction  at  a' .  The  wind  panel  loads  are 
laid  off  on  the  line  4-10',  Fig.  30  {b).  The  magnitudes  of 
the  reactions  are  found  by  drawing  a  vertical  line  through  4 
to  its  intersection  with  a  line  through  10'  parallel  to  ga'. 
The  stresses  in  the  members  are  found  by  computing  the 
stress  diagram  in  the  usual  way.  They  are  as  follows: 


6380 


27 


Fig.  30 


ROOF  TRUSSES 


§81 


Member 

Vector 

Stress 

(Pounds) 

ab,  be,  c  d,  de,  e  f 
b  B ,  B c,  c  C,  Cd,  d D,\ 

4-20 

+  17,200 

0 

De ,  eE,  E /,  fF  ) 

iaB ,  BC,  CD\ 
\DE ,  EE,  EE') 

10-20 

-  16,000 

/£' 

20-21 

-  14,300 

E'e' 

21-22 

-f  12,800 

e'D' 

22-23 

-  12,000 

D' d’  1 

23-24 

+  10,200 

d'C 

24-25 

-  10,000 

C'cr 

25-26 

+  7,700 

c '  B' 

26-27 

-  8,200 

B'  b' 

27-28 

+  5,100 

E'D ' 

10-22 

-  22,300 

D'C' 

10-24 

-  28,700 

C'B ' 

10-26 

-  35,100 

B'  a ' 

10-28 

-  41,500 

fe' 

5-21 

+  23,100 

e'd' 

6-23 

+  28,100 

d'  c' 

7-25 

4-  33,100 

c'  br 

8-27 

+  38,000 

V  a’ 

9-28 

+  36,100 

34.  Combined  Stresses. — In  order  to  find  the  total 
maximum  stresses  in  the  members,  it  is  advisable  to  tabulate 
the  stresses  due  to  the  different  loadings,  as  shown  in 
the  table  on  the  next  page.  Column  1  gives  the  members, 
column  2  gives  the  stresses  in  the  members  due  to  the 
vertical  load,  column  3  gives  the  stresses  due  to  the  wind 
pressure  on  the  expansion  end,  and  column  4  gives  the 
stresses  due  to  the  wind  pressure  on  the  fixed  end.  The 
stresses  given  in  column  5  are  the  sums  of  those  given  in 
columns  2  and  3;  those  given  in  column  6  are  the  sums  of 
those  given  in  columns  2  and  4.  The  stresses  in  column  7 
are  the  maximum  stresses  in  the  members.  They  are  taken 
from  columns  5  and  6,  the  larger  being  taken  in  each  case. 


TABLE  OF  STRESSES  IN  MEMBERS 

( Pounds ) 


1 

2 

3 

4 

5 

6 

7 

Mem¬ 

ber 

Stresses 
Due  to 
Vertical 
Loads 

Stress 
Due  to 
Wind  on 
Expan¬ 
sion  End 

Stress 
Due  to 
Wind  on 
Fixed  End 

Total 
Stress 
Wind  on 
Expansion 
'  End 

Total 
Stress 
Wind  on 
Fixed  End 

Maximum 

Total 

Stress 

a  b 

+  134, 9°° 

+  36,100 

+  17,200 

+  171,000 

+  152,100 

+  171,000 

b  c 

+  134, 9°° 

+  38,000 

+  17,200 

+  172,900 

+  152,100 

+  172,900 

c  d 

+  119,900 

+  33. 100 

+  17,200 

+  153.000 

+  137, 100 

+  153,000 

d  e 

+  104,900 

+  28,100 

+  17,200 

+  133.000 

+  122,100 

+ 133,000 

ef 

+  90,000 

+  23,100 

+  17,200 

+  113,100 

+  107,200 

+ 113,100 

a  B 

-125,300 

-32,700 

— 16,000 

-158,009 

-141,30° 

— 158,000 

B  C 

— 111,400 

—  26,300 

—  16,000 

-137,700 

—  127,400 

-137,700 

CD 

-  97>4°° 

— 19,900 

—  16,000 

-117,300 

-113,400 

-117,300 

DE 

-  83,500 

-13.5°° 

— 16,000 

—  97,000 

-  99,500 

-  99,500 

EF 

—  69,600 

—  7,200 

—  16,000 

—  76,800 

—  85,600 

—  85,600 

bB 

+  11,100 

+  5,100 

0 

+  16,200 

+  11,100 

+  16,200 

B  c 

—  17,800 

—  8,200 

O 

—  26,000 

—  17,800 

—  26,000 

cC 

+  16,700 

+ 

O 

O 

0 

+  24,400 

+  16,700 

+  24,400 

Cd 

—  21,700 

— 10,000 

0 

-  31,700 

—  21,700 

-  31,700 

dD 

+  22,300 

+ 10,200 

0 

+  32>5°o 

+  22,300 

+  32,500 

De 

—  26,300 

— 12,000 

0 

-  38,300 

—  26,300 

-  38,300 

eE 

+  27,800 

+ 12,800 

O 

+  40,600 

+  27,800 

+  40,600 

Ef 

-  3Lioo 

-i4,3°° 

0 

-  45,400 

-  31,100 

—  45,400 

fE 

0 

0 

0 

0 

0 

0 

fE ' 

-  31,100 

0 

-14,300 

-  31,100 

-  45,400 

-  45,400 

E'  e' 

+  27,800 

0 

+  12,800 

+  27,800 

+  40,600 

+  40,600 

e'  D' 

—  26,300 

0 

—  12,000 

—  26,300 

-  38,300 

-  38,300 

D' d' 

+  22,300 

0 

+  10,200 

+  22,300 

+  32,500 

+  32,500 

d'  a 

—  21,700 

0 

—  10,000 

—  21,700 

-'  31,700 

-  30,700 

C'  c' 

+  16,700 

0 

+  7.7°° 

+  16,700 

+  24,400 

+  24,400 

c'  B' 

1 

H 

00 

0 

0 

0 

—  8,200 

—  17,800 

—  26,000 

—  26,000 

B'  b' 

+  11,100 

0 

+  5,100 

+  11,100 

+  16,200 

+  16,200 

FE' 

—  69,600 

—  7,200 

— 16,000 

—  76,800 

—  85,600 

—  85,600 

E'  D' 

-  83,500 

—  7,200 

—  22,300 

—  90,700 

— 105,800 

— 105,800 

D'C' 

-  97,400 

—  7,200 

—  28,700 

— 104,600 

— 126,100 

— 126,100 

a  Br 

— 111,400 

—  7,200 

-35.100 

— 118,600 

-146,500 

-146,500 

B'  a' 

-125,300 

—  7,200 

—41,500 

-132,500 

— 166,800 

— 166,800 

fe' 

+  90,000 

+ 17,200 

+  23,100 

+ 107,200 

+  113,100 

+  113,100 

e' d' 

+ 104,900 

+ 17,200 

+  28,100 

+ 122,100 

+ 133,000 

+  133,00° 

d'  c' 

+  119,900 

+ 17,200 

+  33+00 

+  137, 100 

+  153,000 

+  153,000 

c'  b' 

+  134,900 

+ 17,200 

+  38,000 

+ 152,100 

+ 172,900 

+  172,900 

b'  a' 

+ 134, 9°° 

+ 17,200 

+  36+00 

+ 152,100 

+ 171,000 

+  171,000 

29 

135—26 


30 


ROOF  TRUSSES 


§81 


It  is  not  necessary  to  find  the  minimum  stresses  in  the 
members  of  roof  trusses,  unless  the  stresses  in  some  of  the 
members'  are  reversed  by  the  wind.  The  stress  in  //'is  given 
as  zero.  This  member  simply  serves  to  support  the  bottom 
chord  at  the  center,  and  is  sometimes  omitted. 


THIRD  ILLU STR  ATIVE  EXAMPLE 


35.  Data. — The  third  illustrative  example  will  be  of  the 
same  general  type  as  the  truss  shown  in  Fig.  15.  The  data 


will  be  assumed  as  follows: 

Distance  between  trusses . b  =  18  feet 

Span . I  =  80  feet 

Rise . r  —  20  feet 

Height  of  monitor .  11  feet 

Number  of  panels . n  —  8 

Distance  from  bottom  chord  to  base  of 

columns .  30  feet 


Roofing  material  .  .  Concrete  slab  inches  thick 
Vertical  sides  of  monitor  ....  Glass  skylights 
Dead  load  of  rafters, 

purlins,  and  trusses  .  18  pounds  per  square  foot 

Snow  load . 30  pounds  per  square  foot 

Supports . Columns  fixed  at  the  bottoms 

The  outline  of  the  truss  is  shown  in  Fig.  31. 


36.  Panel  Length. — Since  l  =  80  feet,  r  =  20  feet, 
and  n  —  8,  the  formula  of  Art.  9  gives 


V802  +  4  X  202 

8 


11.18  feet 


37.  Panel  Loads. — The  panel  load  W  for  any  loading 
is  given  by  the  formula  in  Art.  16.  In  the  present  case, 
b  =  18  feet  and  p  =  11.18  feet. 

1.  Dead  Paiiel  Load. — The  dead  load  consists  of  the 
weight  of  the  concrete  slab,  and  that  of  the  rafters,  purlins, 
and  trusses.  In  addition,  the  weight  of  the  vertical  sides  of 
the  monitor  must  be  considered.  The  weight  of  concrete 
per  square  foot  is  given  in  Art.  13  as  12  pounds  per  inch 


§81 


ROOF  TRUSSES 


31 


of  thickness;  since  the  slab  is  2  k  inches  thick,  the  weight  is 
2k  X  12  =  30  pounds  per  square  foot.  The  weight  of  rafters, 
purlins,  and  trusses  is  18  pounds  per  square  foot.  Then,  the 
total  dead  load  on  the 
sloping  portion  is  30 
+  18  =  48  pounds 
per  square  foot,  and 
for  the  dead  panel 
load  Wa  we  have: 

Wd  =  48  X  18  X  11.18 
=  9,660  pounds 
There  are  full  panel 
loads  of  9,660  pounds 
at  b,c,g,c',  and  b', 

Fig.  32  [a) ,  and  half 
panel  loads  of  4,830 
pounds,  at  a,  d,  e,  e’ ,  d',  and  a \  Since  the  half  panel  loads 
at  e  and  d  (and  the  same  applies  to  e’  and  d')  are  in  the  same 
straight  line,  they  will  be  considered  together  in  laying  out 
the  force  polygon  as  though  they  were  both  applied  at  e  (ef 
for  the  other  side).  The  half  panel  loads  at  a  and  a'  must  be 
considered,  since  they  cause  stresses  in  the  columns. 

The  weight  of  the  sides  of  the  monitor  is  8  pounds  per 
square  foot.  (See  Art.  13.)  Then,  for  the  weight  Wm  of 
each  side  per  bay,  we  have 

Wm  =  8x11x  18  =  1,584  pounds 
All  this  weight  is  applied  at  d  and  df ,  but  in  laying  out 
the  force  polygon  it  is  better  to  consider  it  applied  at  e  and  e’ . 

The  effect  of  considering  the  loads  at  d  and  d'  as  applied 
at  e  and  e\  is  to  make  the  stresses  in  the  verticals  de  and 
d'  e'  greater  than  the  actual  stresses  by  the  amount  of  the 
loads  at  d  and  d' .  The  correction  can  easily  be  made  later 
when  the  stresses  are  scaled  from  the  stress  diagram. 

2.  Snow  Pa?iel  Load . — The  snow  load  is  30  pounds  per 
square  foot.  Then,  for  the  snow  panel  load  Ws  we  have 
Ws  =  30  X  18  X  11.18  =  6,037  pounds 
There  are  full  panel  loads  at  b ,  c ,  g ,  c\  and  b\  and  half 
panel  loads  at  a,  d,  e ,  e\  d\  and  a1’.  The  half  panel  loads  at 


0981  ©  ^  U)8Cf9 


§81 


ROOF  TRUSSES 


33 


e  and  d  ( e '  and  d')  will  be  considered  together  as  full  panel 
loads  at  e  ( e' )  in  laying  out  the  force  polygon.  There  is  no 
snow  load  on  the  sides  of  the  monitor. 

3.  Wind  Panel  Load. — Since  the  rise  is  20  feet  and  the  span 
is  80  feet,  the  roof  has  a  i  pitch  or  a  slope  of  1  in  2.  In 
Art.  15,  the  normal  pressure  on  a  roof  having  a  slope  of  1  in  2 
is  given  as  25  pounds  per  square  foot.  Then,  for  the  wind 
panel  load  Ww  on  the  inclined  portion  of  the  roof,  we  have 
Ww  =  25  X  18  X  11.18  =  5,031  pounds 

There  are  full  panel  loads  at  b  and  c ,  and  half  panel  loads 
at  a,  d ,  e,  and  g. 

In  addition  to  the  above,  the  wind  pressure  on  the  vertical 
sides  of  the  monitor  and  the  building  will  be  considered.  It 
is  customary  to  consider  this  pressure  as  horizontal  and  equal 
to  40  pounds  per  square  foot.  The  total  pressure  on  one  bay 
of  one  side  of  the  monitor  is  40  X  18  X  11  =  7,920  pounds, 
one-half  of  which,  3,960  pounds,  may  be  taken  at  each  of  the 
joints  e  and  d.  The  total  pressure  on  one  bay  of  the  vertical 
side  of  the  building  is  40  X  18  X  30  =  21,600  pounds,  one- 
half  of  which,  10,800  pounds,  may  be  taken  at  joint  a. 

38.  Stresses  Due  to  Dead  and  Snow  Loads. — In  this 
example,  as  in  those  preceding,  the  stresses  due  to  the  verti¬ 
cal  loads  will  be  treated  separately  from  those  due  to  the 
inclined  loads.  The  vertical  loads  at  the  different  joints  of 
the  truss  are  shown  in  Fig.  32  (a).  Those  at  a,  b,  c,g,  c' ,  b' , 
and  a'  are  the  sum  of  the  snow  panel  loads  and  the  loads 
due  to  the  weight  of  concrete  slab  and  roof  framing.  The 
loads  at  e  and  e'  include  the  weight  of  the  vertical  sides. 
Since  the  loading  is  symmetrical,  the  reactions  are  equal. 
In  the  present  case  of  vertical  loading,  it  is  customary  to 
assume  that  the  stresses  in  A  B  and  B'  A'  are  zero. 

The  stress  diagram  is  shown  in  Fig.  32  {b).  It  is  drawn 
in  the  same  way  as  though  the  truss  were  simply  supported 
at  a  and  a ',  the  members  A  B  and  B'  A'  being  omitted.  The 

i 

panel  loads  are  laid  off  on  the  line  0-9,  and,  since  the  reac¬ 
tions  are  equal,  the  point  10  is  located  midway  between  0 
and  9.  The  stress  diagram  can  be  drawn  for  joints  a,  b,  and  B 


u 


ROOF  TRUSSES 


§81 


K 


without  difficulty.  It  is  then  necessary  to  consider  joints, 
then  e  and  e' ,  and  then  d.  At  the  latter  joint,  the  stress 
in  df  is  temporarily  assumed  equal  to  19-17' ,  and  the  dia¬ 
gram  19-17' -16' -3-19  is  drawn  in  dotted  lines  for  the  joints  d\ 
joint  D  is  then  considered,  and  the  diagram  16' —17 '-18' -15' —16' 
drawn  in  dotted  lines.  The  point  14  has  already  been  found, 
and  it  is  known  that  15  lies  on  a  line  14-15"  passing 
through  14  and  parallel  to  c  C.  The  point  15  is  then  found  by 
drawing  15-15'  parallel  to  3-16'  to  its  intersection  15  with 
14-15".  The  remainder  of  the  stress  diagram  can  now  be 
drawn  without  further  difficulty.  The  stresses  in  de  and  d' e' , 
as  indicated  by  the  stress  diagram,  are  each  too  large  by 
9,430  pounds,  on  account  of  the  loads  at  d  and  d'  having 
been  considered  as  applied  at  e  and  e' . 

The  stresses  in  the  members  on  one  side  of  the  center,  as 
scaled  from  the  stress  diagram,  are  as  follows: 


Member 

o  t 

Vector 

Stress 

(Pounds) 

EA 

10-  0 

+  64,400 

A  a 

10-  0 

+  64,400 

AD 

10-11 

0 

a  b 

1-12 

+  126,400 

be 

2-13 

+  126,400 

cd 

3-16 

+  147,500 

df 

19-17 

+  147,500 

fe 

19-20 

-  18,300 

dc 

3-19 

(34,500  -  9,400 
+  25,100) 

eg 

4-20 

+  17,600 

a  B 

11-12 

-  113,100 

DC 

10-14 

-  97,400 

CF 

10-18 

-  56,500 

bB 

12-13 

+  15,700 

Be 

13-14 

-  22,200 

eC 

14-15 

+  40,800 

cD 

15-16 

-  34,600 

CD 

15-18 

-  57,700 

dD 

16-17 

+  34,600 

Df 

17-18 

-  106,600 

fF 

18-23 

0 

•  ...  '» 


' 


' 

x’ 


. 

I 


135  §81 


14894 


§81 


ROOF  TRUSSES^ 


35 


39.  Stresses  Due  to  Wind  Doad. — The  diagram  of  the 
truss  and  the  wind  loads  is  shown  in  Fig.  33  (a).  At  joint  a 
there  is  a  horizontal  pressure  of  10,800  pounds  due  to  the 
pressure  against  the  side  of  the  building,  and  also  the 
inclined  pressure  of  pounds,  due  to  the  normal  pressure 
on  the  roof.  At  joipts  b  and  c  there  are  full  inclined  panel 
loads  of  5,031  pounds,  due  to  the  normal  pressure  on  the 
roof.  At  cL  and  e  there  are  inclined  panel  loads  of  pounds 
due  to  the  normal  pressure  on  the  roof,  and  horizontal  pres¬ 
sures  of  3,960  pounds  due  to  the  pressure  against  the  side  of 
the  monitor.  At  the  peak  g  there  is  an  inclined  pressure 
of  ---2”-  pounds.  The  forces  shown  in  dotted  lines  will  be 
explained  later. 

40.  In  finding  the  reactions,  it  is  necessary  to  consider 
the  condition  of  the  columns  at  E  and  E' .  In  Art.  35,  it  is 
stated  that  the  columns  are  fixed  at  the  bottoms,  so  that 
points  of  inflection  may  be  assumed  at  i  and  i ' ,  half  way 
between  A  and  A,  A'  and  E' ,  respectively.  The  reactions  at  i 

and  i'  will  be  inclined,  and  it  is  impossible  to  determine  their 

* 

directions  except  by  means  of  some  arbitrary  assumption  con¬ 
cerning  the  distribution  of  the  forces  between  i  and  i’ .  In 
practice  it  is  frequently  assumed  that  the  horizontal  com¬ 
ponent  of  each  reaction  is  equal  to  one-half  the  sum  of  the 
horizontal  components  of  the  wind  forces.  This  assumption 
probably  gives  the  reactions  as  close  to  their  actual  values  as 
any  other  assumption  that  can  be  made.  It  becomes  neces¬ 
sary,  therefore,  to  find  the  resultant  of  all  the  wind  forces, 
and  then  to  resolve  it  into  two  components,  one  passing 
through  i  and  one  passing  through  i' ,  their  horizontal  com¬ 
ponents  being  equal  to  each  other. 

The  force  polygon  0-1-2 -3 -4-5 -6 -7 -8-9,  Fig.  33  ( b ), 
is  first  laid  out  in  a  convenient  position,  the  first  point,  0 , 
being  located  for  convenience  on  the  line  i  if  connecting  the 
points  i  and  i' .  The  point  P  is  then  chosen  for  a  pole,  and 
is  located  arbitrarily,  to  simplify  the  work,  on  a  horizontal 
line  through  the  last  point,  9,  of  the  force  polygon.  The 
rays  P-0,  P-2,  P-3,  P-4,  P-6,  P-8,  and  P-9  are  now  drawn. 


36 


ROOF  TRUSSES 


81 


The  ray  P-1  is  left  out  because  the  dotted  line  0-2  in  the 
force  polygon  and  ja  in  the  space  diagram  represent  the 
resultant  of  the  forces  0-1  and  1-2 ,  and  this  resultant  can  be 
considered  instead  of  its  two  components.  In  like  manner, 
the  force  4-6  in  the  force  polygon  and  md  in  the  space 
diagram  may  be  considered  instead  of  the  two  components 
4-5  and  5-6;  the  resultant  en  may  be  considered  instead  of 
6-7  and  7-8.  The  line  0-9,  Fig.  33  {5),  gives  the  magnitude 
of  the  resultant  of  all  the  wind  forces;  the  intersection  q  of 
the  end  strings  of  the  funicular  qjklmnp  q,  drawn  in 
the  usual  way,  gives  a  point  in  the  line  of  action  of  the 
resultant.  A  line  is  then  drawn  through  q  parallel  to  0-9 
to  represent  the  resultant.  The  vertical  and  horizontal  com¬ 
ponents  of  0-9  are  given  by  0-s  and  s-9,  Fig.  33  (b).  The 
point  9",  half  way  between  ^  and  9 ,  divides  the  horizontal 
component  of  0-9  into  two  equal  parts,  each  of  which  is  equal 
to  the  horizontal  component  of  one  of  the  reactions. 

41.  The  vertical  components  of  the  reactions  are  found 
by  considering  the  resultant  F  resolved  into  its  vertical  and 
horizontal  components  at  t,  the  intersection  of  its  line  of 
action  with  it'.  The  vertical  component  0-s  is  laid  off 
on  A  E,  vertically  below  i,  so  that  iu  =  0-s.  The  line  u  z7, 
the  vertical  t  v ,  and  horizontal  v  v'  are  then  drawn.  Then  u  v' 
is  the  vertical  component  of  the  reaction  at  z7,  and  v'  i  is  the 
vertical  component  of  the  reaction  at  i.  The  point  10,  where 
a  vertical  through  9"  intersects  vvf,  is  a  point  on  the  lines  in 
the  force  polygon  that  represent  the  reactions.  Drawing  the 
lines  9-10  and  10-0,  the  magnitudes  and  directions  of  the 
reactions  are  found.  The  lines  of  action  of  the  reactions  are 
then  found  by  drawing  ir  through  i  parallel  to  10-0,  and  i'  r 
through  z7  parallel  to  9-10.  The  lines  i  r  and  z 7  r  should 
intersect  on  the  line  of  action  of  the  resultant.  This  is  a 
very  good  check  on  the  work  thus  far. 

The  vertical  components  of  the  reactions  cause  direct 
stresses  in  the  columns.  The  horizontal  components  of  the 
reactions  cause  bending  moments  and  shearing  stresses  in 
the  columns. 


§81 


ROOF  TRUSSES 


37 


42.  In  order  to  find  the  stresses  in  the  members  of  the 
truss  by  the  method  of  the  stress  diagram,  it  is  necessary 
to  treat  the  shearing  stresses  in  the  posts  or  columns  a  i  and 
a!  i’  as  external  forces  applied  at  the  joints  a ,  A ,  a' ,  and  A'. 
To  find  the  values  of  these  shearing  stresses,  vertical  lines 
are  drawn  through  s  and  9 ",  Fig.  33  ( b ),  the  line  s-9"  repre¬ 
senting  the  horizontal  component  of  the  reaction  at  i.  The 
line  drawn  through  s  intersects  a  horizontal  line  drawn 
through  A  at  the  point  s';  the  line  through  9”  intersects 
a  horizontal  line  drawn  |through  a ,  which  in  this  case 
coincides  with  the  chord  of  the  truss,  at  the  point  w. 
The  line  w  s'  is  then  drawn  and  continued  to  the  point  10 ", 
its  intersection  with  i  i’ .  Then,  10"-0 ,  equal  to  13,860 
pounds,  is  equal  to  the  shear  in  a  A  (and  also  in  a'  A')  and 
may  be  represented  as  an  external  force  acting  at  a  (and 
also  at  a'),  as  shown  by  the  dotted  lines  in  the  figure.  The 
shear  in  iA ,  equal  to  13,860  pounds,  is  equal  to  lO'-O;  then, 
the  horizontal  force  acting  at  the  joint  A  due  to  the  shears 
in  a  A  and  A  i  is  equal  to  the  sum  of  these  shears,  which  is 
27,720  pounds.  This  may  be  treated  as  an  external  force  acting 
at  A  (and  A’) ,  as  shown  by  dotted  lines.  Those  portions  of  the 
columns  that  lie  below  A  and  A'  can  be  assumed  to  be  removed 
and  the  direct  stresses  in  them  represented  by  the  vertical 
external  forces  shown  at  A  and  A'.  The  force  polygon  for  the 
external  forces,  including  the  forces  shown  in  dotted  lines  at 
a ,  A ,  a',  and  A ',  is  10-10'-10"-0-l-2-3-4-5-6-7-8-9-9'-9"-10 , 
Fig.  33  (b).  The  stress  diagram  can  now  be  drawn  in  the 
usual  way,  ignoring  the  reaction  at  i  and  z7,  and  considering 
the  parts  iE  and  z7  E'  of  the  posts  to  be  removed.  It  is 
not  necessary  to  draw  the  stress  diagram  for  wind  load  when 
the  wind  is  blowing  on  the  right  of  the  truss;  for  it  is  obvious 
that  when  the  wind  blows  from  the  right,  the  stress  in  any 
member  is  the  same  as  the  stress  in  the  corresponding  mem¬ 
ber  on  the  other  side  of  the  center  when  the  wind  blows  from 
the  left.  The  stresses  in  the  members,  when  the  wind  is 
blowing  from  the  left,  have  the  values  given  in  the  table  on 
page  38,  these  values  having  been  scaled,  as  usual,  from  the 
stress  diagram. 


38 


ROOF  TRUSSES 


§81 


Member 

Vector 

Stress 

(Pounds) 

a  b 

2-12 

4-  63,900 

be 

3-13 

4-  66,400 

cd 

4-16 

+  38,200 

df 

19-17 

+  43,900 

f  e 

19-20 

+  4,000 

eg 

8-20 

+  1,900 

AB 

10-11 

-  39,200 

bB 

12-13 

+  5,600 

Be 

13-14 

-  47,200 

eC 

14-15 

4-  25,200 

cD 

15-16 

'  -  5,800 

CD 

15-18 

-  35,700 

Df 

17-18 

-  43,900 

dD 

16-17 

+  5,800 

ed 

6-19 

4-  1,100 

a  B 

11-12 

-  31,400 

BC 

10-14 

-  25,700 

CF 

10-18 

-  500 

FC 

10-23 

-  500 

C'Bf 

10-26 

4-  11,800 

B'a' 

28-29 

+  11,800 

d'd 

21-  9 

4-  3,100 

d'D' 

22-24 

+  3,100 

D'f 

22-23 

4-  13,000 

CD' 

23-25 

4-  17,400 

d  D> 

24-25 

-  3,100 

d  C 

25-26 

-  12,300 

B'd 

26-27 

4-  39,200 

b'  B' 

27-28 

0 

A'  B' 

10-29 

4-  39,200 

d  g 

20-  9 

4-  3,100 

fd 

20-21 

-  3,300 

d'  / 

21-22 

4-  5,800 

d  d' 

9-24 

4-  5,800 

b'd 

9-27 

-  28,700 

b'  a' 

9-28 

-  28,700 

E  A' 

10-10' 

4-  3,100 

A  a 

10" -11 

4-  30,800 

E'  A' 

9"— 10 

4-  14,900 

A'  a' 

9' -29 

-  12,800 

fF 

18-23 

0 

§81 


ROOF  TRUSSES 


39 


43.  Combined  Stresses. — The  combined  stresses  are 
given  in  the  table  on  page  40.  In  column  2  are  given  the 
stresses  due  to  vertical  loads,  as  found  in  Art.  38.  In 
column  3  are  given  the  stresses  in  all  the  members  due  to 
wind  on  the  left,  as  found  in  Art.  42.  The  combined  or 
total  stresses  in  the  members  when  the  wind  blows  from  the 
left  are  given  in  column  4;  they  are  found  by  adding  alge¬ 
braically  for  each  member  the  stresses  given  for  that  member 
in  columns  2  and  3.  The  combined  or  total  stresses  in  the 
members  when  the  wind  blows  from  the  right  are  given  in 
column  5;  they  are  found  by  taking  for  each  member  the 
stress  given  in  column  4  for  the  corresponding  member  on 
the  other  side  of  the  center.  The  maximum  and  minimum 
combined  stresses  are  given  in  column  6;  the  former  are 
printed  in  heavy  type  for  the  members  on  the  left  of  the 
center;  the  latter  are  printed  in  ordinary  type  for  the  mem¬ 
bers  on  the  right  of  the  center.  The  maximum  stresses, 
given  in  column  6  for  the  members  on  the  left  of  the  center, 
are  the  same  for  corresponding  members  on  the  right  of  the 
center;  so  it  is  necessary  to  give  them  but  once.  The  same 
statement  is  true  as  regards  the  minimum  stresses. 


EXAMPLES  FOR  PRACTICE 

1.  A  truss  having  the  form  shown  in  Fig.  1  has  a  span  of  20  feet 
and  a  rise  of  5  feet.  If  the  trusses  are  8  feet  apart,  and  the  dead  load 
is  40  lb.  per  square  foot,  what  is  the  dead-load  stress  in  a  c? 

Ans.  —3,600  1b. 

2.  A  truss  having  the  form  shown  in  Fig.  2  has  a  span  of  30  feet 

and  a  rise  of  6  feet.  If  the  trusses  are  10  feet  apart,  and  the  ends  are 
fixed  at  the  tops  of  both  walls,  what  is  the  wind  stress  in  be  when  the 
wind  is  coming  from  the  left?  Ans.  +  2,300  lb. 

3.  A  truss  having  the  form  shown  in  Fig.  3  has  a  span  of  36  feet  and 

a  rise  of  12  feet.  If  the  trusses  are  9  feet  apart,  and  the  left  end  of 
each  truss  rests  on  rollers,  what  is  the  wind  stress  in  a  d  when  the  wind 
is  blowing  on  the  left  side  of  .the  truss?  Ans.  — 2,000  lb. 

4.  What  is  the  wind  stress  in  a  d  in  the  truss  described  in  example  3, 
when  the  wind  is  blowing  on  the  right  side  of  the  truss? 

Ans.  —  2,600  lb. 


TABLE  OF  STRESSES 

( Pounds ) 


1 

2 

3 

4 

5 

6 

Mem¬ 

ber 

Stress  Due 
to  Vertical 
Loads 

Stress 

Due  to 
Wind  on 
Left 

Combined 
Stress 
Wind  on 
Left 

Combined 
Stress 
Wind  on 
Right 

Maximum 

or 

Minimum 

Combined 

Stress 

a  b 

+ 

126,400 

+  63,900 

+ 

190,300 

+ 

97,700 

+ 

190,300 

b  c 

+ 

126,400 

+  66,400 

+ 

192,800 

+ 

97,700 

+ 

192,800 

c  d 

+ 

147,500 

+  38,200 

+ 

185,700 

+ 

153,300 

+ 

185,700 

df 

+ 

147,500 

+  43,900 

+ 

191,400 

+ 

153,300 

+ 

191,400 

fe 

— 

18,300 

+  4,000 

— 

14,300 

— 

21,600 

— 

21,600 

eg 

+ 

17,600 

+  1,900 

+ 

19,500 

+ 

20,700 

+ 

20,700 

A  B 

0 

-39,200 

— 

39,200 

+ 

39,200 

+ 

39,200 

b  B 

+ 

i5>7°° 

+  5,600 

+ 

21,300 

+ 

15,700 

+ 

21,300 

B  c 

— 

22,200 

—  47,200 

— 

69,400 

+ 

17,000 

— 

69,400 

cC 

+ 

40,800 

+  25,200 

+ 

66,000 

+ 

28,500 

+ 

66,000 

cD 

% 

34,600 

-  5,800 

— 

40,400 

— 

37,700 

— 

40,400 

CD 

— 

57,700 

-35,7oo 

— 

93,400 

— 

40,300 

— 

93,400 

Df 

— 

106,600 

-43,900 

— 

150,500 

— 

93,600 

— 

150,600 

dD 

+ 

34,600 

+  5,800 

+ 

40,400 

+ 

37,700 

+ 

40,400 

e  d 

+ 

25,100 

+  1,100 

+ 

26,200 

+ 

28,200 

+ 

28,200 

a  B 

— 

113,100 

-31,400 

— 

144,500 

— 

101,300 

— 

144,500 

B  C 

— 

97,400 

-25,700 

— 

123,100 

— 

85,600 

— 

123,100 

C  F 

— 

56>5°° 

-  5°° 

— 

57,00° 

— 

57,ooo 

— 

57,000 

F  C' 

— 

56>5°° 

—  5°° 

— 

57,ooo 

— 

57,ooo 

— 

56,500 

C'B' 

— 

97,400 

+ 11,800 

— 

85,600 

— 

123,100 

— 

85,600 

B'  a ' 

— 

113,100 

+ 11,800 

— 

101,300 

— 

144,500 

— 

101,300 

d'  e' 

+ 

25,100 

+  3>IO° 

+ 

28,200 

+ 

26,200 

+ 

25,100 

d'  D' 

+ 

34,600 

+  3>IO° 

+ 

37,7oo 

+ 

40,400 

+ 

34,600 

D'f 

— 

106,600 

+ 13,000 

— 

93,600 

— 

150,500 

— 

93,600 

C'  D' 

— 

57»7oo 

+ 17,400 

— 

40,300 

— 

93,400 

— 

40,300 

c'  D' 

— 

34,600 

-  3,100 

— 

37,7oo 

— 

40,400 

— 

34,600 

c'  C' 

+ 

40,800 

-12,300 

+ 

28,500 

+ 

66,000 

+ 

28,500 

B'c' 

— 

22,200 

+  39,200 

+ 

17,000 

— 

69,400 

+ 

17,000 

b'  B' 

+ 

15.700 

0 

+ 

15,700 

+ 

21,300 

+ 

I5,700 

A'  B' 

0 

+  39,200 

+ 

39,200 

— 

39,200 

— 

39,200 

e'  g 

+ 

17,600 

+  3, 100 

+ 

20,700 

+ 

19,500 

+ 

17,600 

fe' 

— 

18,300 

--  3,3oo 

- 

21,600 

— 

14,300 

— 

14,300 

d'f 

+ 

147,500 

+  5,800 

+ 

i53,3oo 

+ 

191,400 

+ 

147,500 

c' d' 

+ 

147,500 

+  5,800 

+ 

i53,3oo 

+ 

185,700 

+ 

147,500 

b '  c' 

+ 

126,400 

—  28,700 

+ 

97,7oo 

+ 

192,800 

+ 

97,700 

b'  a' 

+ 

126,400 

—  28,700 

+ 

97,7oo 

+ 

190,300 

+ 

97,700 

EA 

+ 

64,400 

+  3, 100 

+ 

67,500 

+ 

79,3oo 

+ 

79,300 

A  a 

"4~ 

64,400 

+  30,800 

+ 

95,200 

+ 

51,600 

+ 

95,200 

E'  A' 

+ 

64,400 

+ 14,900 

+ 

79,3oo 

+ 

67,500 

+ 

64,400 

A' a' 

+ 

64,400 

— 12,800 

+ 

51,600 

+ 

95,200 

+ 

5 1 .600 

0 

0 

0 

0 

0 

40 


81 


ROOF  TRUSSES 


41 


DESIGN 


TRUSSES  AND  LATERAL  SYSTEMS 

44.  Kinds  of  Trusses. — Roof  trusses  are  made  of  wood 
and  of  steel.  The  kind  of  material  used  depends  on  the 
particular  conditions  in  each  case.  In  temporary  buildings, 
and  in  buildings  that  are  not  required  to  be  fireproof,  wooden 
trusses  may  be  used.  In  all  permanent  work  of  any  impor¬ 
tance,  and  in  all  fireproof  buildings,  steel  trusses  are  used. 
Riveted  trusses  are  used  for  short  spans,  less  than  75  to 
100  feet,  and  pin-connected  trusses  for  long  spans,  greater 
than  75  to  100  feet.  The  dividing  line  between  these  two 
kinds  of  trusses  is  not  so  clearly  defined  in  the  case  of  roof 
trusses  as  in  the  case  of  bridge- trusses.  In  general,  riveted 
trusses  are  preferable  when  the  stresses  in  some  of  the 
members  are  reversed  by  the  wind. 

45.  Working  Stresses.  —  The  allowable  or  working 
stresses  for  steel  roof  trusses  are  the  same  as  those  given  for 
highway  bridges  in  Bridge  Specifications.  The  working 
stresses  for  wooden  roof  trusses  are  the  same  as  those 
given  in  Wooden  Bridges. 

46.  Design  of  Main  Members. — The  same  general 
types  of  members  are  used  for  roof  trusses  as  for  bridge 
trusses.  In  addition,  loop-welded  rods  are  sometimes  used 
for  main  members.  The  principal  difference  lies  in  the  fact 
that,  as  the  stresses  in  the  members  of  roof  trusses  are,  as  a 
rule,  less  than  the  stresses  in  the  members  of  bridge  trusses, 
the  members  in  the  former  are  smaller  than  in  the  latter. 
For  this  reason,  roof  trusses  are  much  narrower  than  bridge 
trusses,  and  in  the  shorter  spans,  the  web  members  are 
connected  to  the  chord  and  rafter  by  means  of  one  web 
connection  plate  instead  of  two.  The  principles  that  govern 
the  design  of  the  main  members  of  roof  trusses  are  the 


ROOF  TRUSSES 


42 


same  as  those  that  have  been  illustrated  and  explained  in 
connection  with  bridge  design. 

47.  [Lateral  Systems. — Roof  trusses  are  connected  by 
lateral  bracing  in  the  planes  of  the  rafters,  by  transverse 
bracing  between  the  trusses  in  vertical  planes  or  at  right 
angles  to  the  rafters,  and  in  some  cases  by  lateral  bracing 
in  the  plane  of  the  lower  chord.  The  same  general  style  of 
bracing  is  used  as  for  bridge  trusses;  but,  there  being, 
as  a  rule,  more  roof  trusses  in  a  roof  than  bridge  trusses 
in  a  bridge,  the  arrangement  of  the  lateral  systems  is  some¬ 
what  different. 


It  is  customary  to  insert  lateral  trusses  in  each  end  bay, 
and  also  in  every  second  or  third  intermediate  bay  through¬ 
out  the  length  of  the  building,  as  shown  in  Fig.  34.  The 


figure  is  the  plan  of  the  roof  of  a  building:  A  A'  and  B  B'  are 
the  end  trusses,  and  C  C  are  the  intermediate  trusses.  The 
purlins  A  B,  D  D' ,  and  A'  B’  run  the  entire  length  of  the 
building,  being  spliced  at  each  truss,  or  at  every  other  truss. 
The  common  rafters  that  run  at  right  angles  to  the  purlins 
are  not  shown  in  the  figure.  The  end  bays  and  every  second 
bay  throughout  the  building  are  supplied  with  lateral  trusses. 
The  lateral  truss  in  each  end  bay  is  designed  to  resist  the 
wind  pressure  on  that  end  of  the  building;  the  other  lateral 
trusses  are  then  made  the  same  as  those  in  the  end  bays. 
Lateral  and  loop-welded  rods  are  frequently  used  for  the 
diagonals  of  lateral  systems  of  roofs. 


a 


Lap  Screw- 


Bloch  32*8*8$ 


I 2  Bolt  Upset, 


Fig.  40 


44 


ROOF  TRUSSES 


81 


CONNECTIONS 


»•  *  '  *  ‘ 

WOODEN  TRUSSES 

48.  Rafter  Joints. — Figs.  35  to  40  show  typical  joints 
for  the  rafters  of  wooden  trusses.  In  Fig.  35,  the  purlin, 
shown  in  cross-section,  is  placed  on  top  of  the^  rafter  and 
at  right  angles  to  it.  Both  the  purlin  and  rafter  are  framed 
where  they  connect.  The  purlin  is  held  in  position  by  the 
inclined  brace  a.  The  vertical  rod  b  passes  through  the 
rafters,  and  the  strut  c  is  cut  at  the  end  to  fit  into  a  shoulder 
cut  in  the  bottom  of  the  rafter. 

In  Fig.  86,  the  purlin  is  attached  to  the  rafters  by  means  of 
the  beam  hanger  b.  The  inclined  strut  c  is  connected  to  the 
castings  that  bears  against  the  rafter.  In  Fig.  37,  a  wooden 
blocks  is  inserted  in  the  bottom  of  the  rafter,  and  the  inclined 
strut  c  is  connected  to  it  by  means  of  the  bolt  b.  The  end 
of  the  strut  fits  into  a  triangular  hole  cut  in  the  block. 

In  Figs.  38  and  39,  the  purlins  are  not  shown;  these  figures 
show  methods  of  providing  a  greater  bearing  area  for  the 
upper  ends  of  the  vertical  rods  and  inclined  struts  by  means 
of  plates  and  castings. 

Fig.  40  shows  the  connection  when  the  rod  is  inclined  and 
the  strut  is  vertical.  In  this  figure,  the  purlin  is  shown 
vertical,  and  one  side  of  it  is  in  contact  with  the  casting  b 
that  provides  a  bearing  for  the  inclined  rod  a. 

49.  Peak  Joint. — The  joint  at  the  top  of  a  roof  truss 
is  usually  called  the  peak  joint.  Figs.  41  to  45  show 
several  peak  joints.  In  Fig.  41,  the  rod  c  passes  between 
the  ends  of  the  two  rafters  a  and  b;  the  plate  d  provides 
a  bearing  for  the  end  of  the  rod.  In  Fig.  42,  the  plates  a 
are  bolted  to  the  sides  of  the  rafter  sticks  to  assist  in  * 
holding  them  in  place.  In  Fig.  43,  the  upper  ends  of  the 
rafter  members  are  cut  off  square  and  bear  on  a  casting  a. 
The  rods  (two  in  this  case)  pass  through  flanges  in  the 
casting,  and  are  held  in  place  by  the  nuts  b.  The  chair  or 


Fig.  43 


45 


46 


ROOF  TRUSSES 


§81 


shelf  c  is  for  the  purpose  of  supporting  the  ends  of  the ' 
purlins.  Fig.  44  shows  another  method  of  connecting  the 

tension  rods  and 
compression  mem¬ 
bers;  in  the  form  of 
connection  here  rep¬ 
resented,  gussets  or, 
connection  plates  a 
are  bolted  to  the  sides 
of  the  rafter  sticks, 
and  the  inclined 
rods  b  are  connected 
fig.  46  to  them  by  means  of 

pins  c,  which  pass  through  the  gussets.  The  vertical  rod 
passes  through  the  sticks  and  bears  on  the  plate  d  in  the 
same  way  as  in 
Fig.  41.  In  the  con¬ 
nection  shown  in 
Fig.  45,  the  rafter 
sticks  bear  against 
the  casting  a ,  and  the 
inclined  rods  con- 
i  nect  to  the  pin  b  that 
passes  through  the 
casting.  The  vertical 
rod  is  connected  by 
a  pin  c  to  a  projection  on  the  casting  at  the  bottom. 

50.  Chord  Joints. — Figs.  46  and  47  show  the  connec¬ 
tions  of  a  vertical  rod, 
two  inclined  struts, 
and  the  chord.  The 
blocks  c  are  set  into 
the  top  of  the  chord 
and  beveled  on  the 
ends  to  give  the 
struts  a  square  bear¬ 
ing.  The  dowels 

•  shown  in  Fig.  47  are  sometimes  omitted. 


§81 


ROOF  TRUSSES 


47 


51.  Heel  Joints. — The  end  joint  of  a  roof  truss,  where 
the  rafter  and  the  chord  connect,  is  sometimes  called  the 
lieel.  Fig.  48  shows  the  simplest  form  of  heel  joint.  Fig.  49 
shows  a  very  good  joint  where  the  inclined  member  is 
composed  of  two 
sticks.  Both  the  in¬ 
clined  sticks  and  the 
horizontal  chord  are 
cut  away  so  as  to 
form  shoulders,  and 
the  ends  of  the  sticks 
are  bolted  together. 

Fig.  50  shows  a 
form  of  heel  joint  that  is  used  when  the  roof  has  a  flat  slope 
and  it  is  not  desired  to  cut  too  much  into  the  end  of  the  chord. 


The  casting  dd  is  fitted  and  bolted  to  the  top  of  the  chord, 
and  provides  a  bearing  for  the  inclined  stick.  A  short  piece 
of  timbers  is  bolted  and  keyed  to  the  bottom  of  the  chord  by 
the  bolts  a  and  the  keys  k ,  k.  The  bolt  g  is  not  assumed  to 


48 


ROOF  TRUSSES 


81 


transmit  any  stress;  it  is  simply  for  the  purpose  of  holding 
the  lower  end  of  the  inclined  member  in  place. 


The  joint  shown  in  Fig.  51  is  somewhat  similar  to  that 
shown  in  Fig.  50;  but  the  method  of  providing  a  bearing  for 

the  rafter  is  different. 
In  Fig.  51,  the  purlin  a 
is  shown  on  top  of  the 
rafter  b;  the  common 
rafter  c  with  the  roof 
covering  d  is  on  top  of 
the  purlins. 

52.  Combination 
Chord  Joint. — Fig.  52 
shows  a  chord  joint  of  a 
truss  in  which  the  com¬ 
pression  members  are  wood  and  the  tension  members  steel. 
Pin  plates  a  are  bolted  on  the  sides  of  the  stick  b ,  and  the 
ends  of  all  the  members  are  connected  by  the  pin  c. 


§  si  ROOF  TRUSSES  49 

STEEL  TRUSSES 

53.  Rafter  Joint. — Figs.  53  to  57  show  rafter  joints 
of  steel  roof  trusses.  In  Fig.  53,  a  wooden  purlin  is 
shown  in  cross-section;  it  is  held  in  place  by  the  bracket  a. 


The  rafter  in  this  case  consists  of  a  single  web  b  and 
two  top  flange  angles  c.  The  web  members  are  riveted 
directly  to  the  web-plate,  and  there  is  no  need  of  a  gusset. 

Fig.  54  shows  the  method 
of  connecting  a  steel  purlin  a 
to  the  rafter  by  means  of  the 


Fig.  54  Fig.  55 

connection  angle  b.  This  figure  also  shows  the  wooden  com¬ 
mon  rafter  c  on  top  of  the  purlin,  held  in  place  by  the  steel 
clip  d.  Fig.  55  shows  another  method  of  connecting  a  pur¬ 
lin  a  to  the  truss.  In  this  case,  a  gusset  b  is  used  for  the 
connection  of  the  web  members  to  the  rafter.  In  Fig.  56, 


50 


ROOF  TRUSSES 


the  purlin  a  is  shown  vertical,  and  the  common  rafter  b  is  con¬ 
nected  to  it  by  means  of  a  clip. 

Fig.  57  is  a  rafter  joint  in  a  pin-connected  truss.  Both 


the  rafter  and  the  compres¬ 
sion  .  web  member  are  com¬ 
posed  of  two  channels.  The 
rafter  is  spliced  at  this  joint, 
being  cut  at  the  center  of  the 
pin.  This  splice  is  simply  for 
the  purpose  of  decreasing  the 
length  of  the  rafter  pieces,  so 
that  they  can  be  handled  more 
easily.  The  compression  web 
member  is  connected  to  the 
pin  by  means  of  pin  plates. 


54.  Peak  Joint. — Figs.  58  and  59  are  peak  joints  of 
riveted  trusses,  and  show  how  the  members  are  connected 


at  the  top.  In  Fig.  58,  the  rafter  members  are  each  com¬ 
posed  of  two  angles,  and  the  vertical  member  is  composed 


§81 


ROOF  TRUSSES 


51 


of  two  flat  bars.  The  gusset  a  is  riveted  in  the  shop  to  one 
of  the  rafter  members,  and  the  other  members  are  riveted  to 
it  in  the  field.  The  purlin  c  is  composed  of  two  channels,  and 
is  connected  to  the  truss 
by  means  of  the  bent 
bars  d.  This  joint  also 
shows  the  way  in  which 
the  common  rafters  b 
may  be  connected  to 
the  top  of  the  purlin. 

Fig.  59  is  the  peak 
joint  of  a  much  larger 
truss.  The  vertical 
webs  a>  a  that  form  part 
of  the  section  of  the 
rafter  are  spliced  at  b}  b 
to  the  gusset  c.  The  gusset  is  shown  connected  at  the  left 
end  of  the  rafter  and  one  of  the  web  members  by  shop  rivets, 
and  to  all  the  other  members  by  means  of  field  rivets.  It  is 
customary  to  rivet  as  great  a  portion  of  a  roof  truss  together 


Fig.  59 


in  the  shop  as  can  be  conveniently  transported  to  the  place 
where  it  is  to  be  erected. 

55.  Heel  Joint. — Fig.  60  shows  a  method  of  forming 
the  heel  joint  of  a  riveted  truss  when  the  end  rests  on  a 
pedestal  or  on  the  wall.  The  chord  a  is  continued  across 


52 


ROOF  TRUSSES 


§81 


the  support,  and  the  rafter  b  is  connected  to  it  by  means  of 
the  gusset  c.  Fig.  61  shows  a  method  of  forming  this  joint 


when  the  end  of  the  truss  is  supported  on  a  column.  The 
rafter  a  is  continued  across  the  top  of  the  column,  and  the 
angles  or  other  shapes  b  of  which  the  column  is  composed 


are  continued  up  to  the  under  side  of  the  rafter.  The  gusset  c 
connects  the  end  of  the  chord  and  that  of  the  rafter  to  the 
top  of  the  column.  In  the  figure,  the  web  of  the  column 
is  stopped  at  dd ,  and  the  lower  edge  of  the  gusset  is  inserted 
between  the  angles  at  the  top.  The  gusset  and  web-plate 
are  spliced  by  the  side  plates  e\  when  there  are  no  side 
plates,  additional  plates  are  used  for  splicing. 


§81 


ROOF  TRUSSES 


53 


56.  Chord  Joints. — Fig.  62  shows  a  method  of  form¬ 
ing  a  chord  joint  of  a  pin-connected  roof  truss.  In  this  joint, 
all  the  tension  members  are  placed  inside  the  channels  that 


form  the  compression  member.  Fig.  63  shows  a  chord  joint 
of  a  riveted  roof  truss,  the  chord  being  spliced  at  the  joint. 
In  this  figure,  every  member  is  composed  of  two  angles; 


the  ends  are  connected  by  a  single  gusset  inserted  between 
the  angles.  This  gusset  acts  also  as  a  splice  plate  for  the 
chord. 


BRIDGE  PIERS  AND  ABUTMENTS 


PRELIMINARIES 


DEFINITIONS 

1.  Abutments  and  Piers.— The  supports  provided  for 
the  ends  of  a  bridge  are  generally  required  to  hold  back  the 
banks,  thus  acting  both  as  supports  for  the  bridge  and  as 


Fig.  1 


retaining  walls;  supports  of  this  character  are  shown  at  A 
and  A,  Fig.  1,  and  are  called  abutments.  When,  as  at  inter¬ 
mediate  points,  such  as  £,  C,  E>,  and  E ,  Fig.  1,  there  is  no 
bank  to  restrain,  the  supports  are  called  piers. 

INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 


COPYRIGHTED  BY 


2 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


2.  An  abutment  usually  has  lateral  extensions,  a ,  a , 
Fig.  1  (a) ,  to  hold  back  the  earth  in  the  sloping  bank.  These 
extensions  are  called  wings,  and  the  abutment  is  some¬ 
times  called  a  wing  abutment,  if  it  is  desired  to  indicate 
the  existence  of  wings.  Nearly  all  abutments  are  wing 
abutments. 

When  the  wings  are  omitted,  as  at  A,  Fig.  1  ( a ),  and  the 
filling  material  is  allowed  to  run  around  in  front  of  the  abut¬ 
ment,  the  latter  is  called  a  pier  abutment,  or  abutment 
pier. 

3.  Piers  may  be  carried  up  to  such  a  height  as  to  give  a 
direct  support  to  the  bridge,  as  at  C  and  D,  Fig.  1  (3),  or 
they  may  be  carried  only  to  such  a  height  as  to  protect  the 
structure  from  the  destructive  influences  below  or  near  the 
surface  of  the  earth,  as  at  B  and  E ,  a  trestle  b ,  b  being  intro¬ 
duced  between  the  top  of  the  pier  and  the  bottom  of  the 
bridge.  These  low  piers  are  frequently  divided  into  two 
separate  supports,  as  shown  at  A',  Fig.  1  {a) ,  called  pedestals, 
or  pedestal  piers. 

4.  Superstructure  and  Substructure. — The  bridge 
proper,  which  rests  on  the  piers  and  abutments,  above  the 
level  G  G,  Fig.  1  (b),  is  called  the  superstructure.  All 
supporting  work  below  the  level  G  G,  including  trestles  or 
columns,  as  at  B  and  A,  and  all  the  masonry,  is  called  the 
substructure . 

5.  Bridge  Seat. — The  top  surface  /, /,  Fig.  l'(£),of  an 
abutment  or  pier  to  which  the  weight  of  the  bridge  is  directly 
transmitted  is  called  the  bridge  seat.  The  course  g,  g  of 
masonry  directly  under  the  bridge  seat  is  called  the  bridge- 
seat  course,  coping  course,  or  top  course;  it  is  some¬ 
times  called  simply  the  bridge  seat  or  coping.  This  course 
usually  projects  a  few  inches  beyond  the  outer  edge  of  the 
masonry  directly  under  it.  This  projection  is  called  the 
overhang  of  the  bridge  seat;  it  improves  the  appearance 
of  the  pier,  and  protects  the  masonry  beneath  it  from  the 
weather.  The  outer  edge  h,h,  Fig.  1  (a),  of  the  masonry 
immediately  under  the  top  course  is  called  the  neat  line. 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


3 


6.  Pedestal  Blocks. — In  cases  where  stringers  or  floor- 
beams  rest  on  the  masonry  at  elevations  different  from  the 
elevations  of  the  base  of  the  trusses  or  girders,  separate  top 
courses  are  sometimes  laid;  but  more  frequently  the  top 
course  is  finished  level  at  the  proper  elevation  for  the  trusses 
or  girders,  and  is  called  the  main  bridge  seat.  The 
proper  elevation  is  then  secured  for  the  stringers  or  floor- 
beams  by  placing  stone  blocks,  called  pedestal  blocks,  on 
top  of  the  main  bridge  seat.  In  many  cases,  the  desired 
elevation  is  secured  by  means  of  steel  castings,  called 
pedestals. 

7.  Parapet. — In  order  to  keep  the  filling  from  running 
over  on  the  bridge  seat,  a  back  wall  c,  c,  Fig.  1,  commonly 
called  a  parapet,  is  usually  built  on  top  of  the  bridge  seat. 

8.  Footings. — The  lower  part  dy  d}  Fig.  1  (b) ,  of  a  pier 
or  abutment  is  called  the  footing.  It  is  usually  made  to 
project  somewhat  beyond  the  masonry  of  the  main  body 
above  it.  Footings  serve  the  purpose  of  securing  greater 
bearing  area  on  the  soil  and  of  giving  greater  stability  to 
the  structure. 

9.  Cutwaters. — When  piers  are  placed  in  running 
streams,  as  at  D,  Fig.  1,  they  are  usually  placed  with  their 
longest  dimension  parallel  to  the  direction  of  the  current, 
and  the  ends  are  made  pointed  instead  of  flat,  in  order 
to  reduce  the  obstruction  to  the  flow  of  water.  The 
up-stream  end  is  generally  made  sharper  than  the  down¬ 
stream  end.  The  sharp  ends  e,  e,  Fig.  1  (a),  are  called 
nosings  or  cutwaters.  In  cold  climates,  where  floating  ice 
is  common,  cutwaters  are  sometimes  called  ice  breakers, 
and  are  frequently  protected  by  means  of  a  bent  steel  plate 
fastened  to  the  masonry.  This  protection  should  always 
be  provided  where  large  masses  of  ice  are  likely  to  float 
down  the  stream. 


4 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


LOCATION  AND  ESTIMATES 

10.  Direction  of  Crossing. — The  direction  of  a  bridge, 
especially  of  a  railroad  bridge,  should,  if  practicable,  be  so 
selected  that  the  crossing  will  be  at  right  angles,  or  nearly 
so,  to  the  direction  of  the  stream,  road,  or  depression  to 
be  crossed.  This  is  desirable  both  because  such  location 
reduces  the  length,  and  accordingly  the  cost,  of  the  structure, 
and  also  because  a  skew  end  is  objectionable  from  a  purely 
structural  point  of  view.  The  problem  of  making  the  crossing 
square  or  nearly  so  is  not  always  considered  the  duty  of  the 
bridge  engineer;  but  the  locating  engineer  should  endeavor 
so  to  arrange  the  alinement  as  to  avoid  the  necessity  of  skew 
bridges. 

11.  In  the  case  of  a  railroad  bridge,  unless  it  is  made 
unusually  heavy  and  stiff,  the  rigidity  of  the  support  at  the 
abutment  and  the  elasticity  of  the  unsupported  part  of  the 
bridge  at  the  opposite  side  cause  an  undesirable  swing  to 
passing  trains.  The  cause  of  this  swing  may  be  understood 


account  of  the  rigidity  of  the  abutments,  the  deflection  at 
such  a  point  as  A  is  practically  negligible,  while  at  such  a 
point  as  A,  directly  opposite  A ,  the  truss  deflects  an  appre¬ 
ciable  amount.  The  result  is  that  the  floor,  and  conse¬ 
quently  the  train,  is  inclined  sidewise  from  A  to  B.  This 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


5 


objectionable  condition  may  sometimes  be  avoided  by  squar¬ 
ing  up  the  ends,  as  shown  by  dotted  lines  in  Fig.  2,  but  this 
still  further  lengthens  and  increases  the  cost  of  the  crossing; 
and,  if  more  than  one  span  is  required,  the  intermediate  piers 
must  still  be  generally  left  on  a  skew,  so  as  to  present  as 
little  obstruction  as  possible  to  the  current  or  traffic  beneath. 

12.  Location  of  Piers. — With  the.  location  of  the 
crossing  determined,  the  problem  is  not  necessarily  wholly 
solved.  If  the  bridge  is  over  a  railroad,  a  highway,  or  a 
navigable  stream,  the  position  and  length  of  one  or  more 
spans  may  be  fixed  by  the  requirements  of  the  traffic  beneath; 
for  the  way  previously  existing  is  entitled  to  the  prefer¬ 
ence  and  controls  to  a  great  extent  the  locations  and  dimen¬ 
sions  of  the  piers.  The  first  thing  to  do  after  the  direction 
and  location  of  the  crossing  have  been  decided  is  to  deter¬ 
mine  the  location  of  the  abutments,  and  to  ascertain  to  what 
extent  the  traffic  underneath  will  affect  the  selection  of  the 
number  and  length  of  spans.  The  piers  should  be  located  so 
as  to  offer  the  least  possible  amount  of  obstruction.  This 
condition  frequently  controls  the  location  of  every  pier. 
Another  element  that  must  be  taken  into  account  in  deter¬ 
mining  the  positions  and  number  of  piers  is  the  cost.  It 
should  be  borne  in  mind  that  a  reduction  in  the  number  of 
piers  requires  an  increase  in  the  lengths  of  the  spans,  and 
that  the  increased  cost  of  the  spans  may  upset  the  saving 
resulting  from  a  reduction  in  the  number  of  piers.  If  the 
crossing  is  a  low  one,  and  a  good  foundation  can  be  obtained 
at  a  moderate  depth,  short  spans  are  often  more  economical 
than  long  spans. 

13.  Economical  Arrangement. — For  preliminary 
estimates,  use  may  be  made  of  the  empirical  rule  that  the 
economic  arrangement  is  approximately  that  in  which  the 
cost  of  the  substructure  equals  the  cost  of  the  superstructure 
(the  trestles,  if  any,  being  included  in  the  substructure). 
Also,  in  this  preliminary  study,  the  cost  of  the  main  trusses 
or  girders  may  be  considered  as  varying  directly  as  the 
square  of  the  span,  and  the  cost  of  the  floor  directly  as  the 


6 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


length  of  the  span,  unless  the  change  of  length  of  spa?i  is  suffi¬ 
cient  to  change  the  character  of  the  structure.  The  cost  of  the 
substructure  for  any  one  support  depends  on  the  length  of 
span,  the  height  of  the  structure,  and  the  depth  of  the  founda¬ 
tion.  By  roughly  designing  piers  for  both  the  longest  and 
the  shortest  span  to  be  considered,  the  cost  of  each  pier  can 
be  approximately  determined. 

If  the  crossing  is  short,  the  most  economical  number  of 
spans  and  length  of  span  may  generally  be  determined 
immediately  by  finding  a  span  such  that  the  total  cost  of  sub¬ 
structure  divided  by  the  length  of  the  bridge  will  be  approx¬ 
imately  equal  to  the  total  cost  of  superstructure  divided  by 
the  length  of  the  bridge.  But  if  the  crossing  is  long,  a  more 
detailed  estimate  of  cost  is  usually  necessary. 

14.  Approximate  Costs. — For  the  purpose  of  com¬ 
parison,  the  cost  of  masonry  for  the  substructure  and  of  the 
steelwork  for  the  superstructure  may  be  assumed.  In  this 
Section,  the  cost  of  the  masonry  will  be  taken  as  $10  per 
cubic  yard,  and  that  of  the  excavation  for  foundations  as 
50  cents  per  cubic  yard,  including  the  disposal  of  the  material 
excavated.  For  rough  estimates,  the  cost  per  linear  foot  of 
the  steelwork  of  the  bridge  spans  and  the  necessary  dimen¬ 
sions  of  bridge  seat  for  different  spans  may  be  taken 


approximately  as 

Span 

Feet 

follows: 

Cost  per 

Required  Size 

-  Linear  Foot 
Dollars 

of  Bridge  Seat 
Feet 

50 

50 

4  X  10 

100 

80 

5  X  15 

150 

110 

6  X  20 

200 

140 

7  X  25 

250 

170 

8  X  30 

ILLUSTRATIVE  EXAMPLE 

15.  Data. — As  an  illustration,  let  it  be  assumed  that  a 
bridge  1,000  feet  long  for  a  single-track  railroad  is  to  be 
built  across  a  valley  80  feet  deep,  the  masonry  to  be  carried 


» 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


/ 


to  a  depth  of  5  feet  below  the  bottom  of  the  valley  and  up  to 
such  height  as  to  give  direct  support  to  the  bridge  span; 
and  the  distance  between  the  tops  of  piers  and  the  base  of 
rails  to  be  one-fifth  of  the  length  of  the  spans. 

i 

16.  Possible  Spans. — It  will  be  readily  seen  that  a 
length  of  1,000  feet  may  be  divided  into  two  spans  of  500 
feet  each,  or  three  spans  of  383  feet  4  inches,  or  four  spans 
of  250  feet,  or  any  greater  number  of  spans  of  correspond¬ 
ingly  shorter  length.  But  it  is  also  obvious  that  with  the 
longer  spans  the  cost  of  the  superstructure  will  be  much 
greater  than  if  short  spans  are  used. 

17.  Cost  of  Superstructure  and  Substructure. — For 
rough  estimates  of  this  kind,  it  is  sufficiently  close  to  assume 
the  top  of  the  pier  to  have  the  dimensions  given  for  the  bridge 
seat,  and  the  four  sides  to  have  a  batter  of  1  inch  per  foot 
down  to  the  level  of  the  ground;  whence,  with  an  offset  of 
1  foot  on  each  side  and  one  at  each  end,  the  same  dimensions 
are  maintained  down  to  the  subfoundation,  5  feet  below  the 
ground  surface.  With  these  assumptions,  the  approximate 
quantities  and  cost  for  the  substructure  are  found  to  be  as 
given  in  the  following  table: 


Span 

Feet 

Masonry 

Excavation 

Total 
Cost 
per  Pier 

Total  Cost 
of  Sub¬ 
structure,  per 
Foot  of  Span 

Total  Cost 
of  Super¬ 
structure  per 
Foot  of  Span 

Cubic 

Yards 

Cost 

Cubic 

Yards 

Cost 

50 

510 

$5UOO 

78 

$39 

$5,139 

$102.80 

$  50 

75 

533 

5,330 

82 

4i 

5,371 

71 .60 

65 

IOO 

548 

5,480 

85 

43 

5,523 

55-20 

80 

150 

558 

5,58o 

92 

46 

5,626 

37.50 

I  IO 

200 

537 

5,370 

98 

49 

5,419 

27.10 

140 

250 

488 

4,880 

103 

5i 

4,931 

19.70 

170 

18.  In  finding  the  quantities  given  in  the  second  column 
of  the  table,  it  is  convenient  to  draw  a  diagram  similar  to 
that  shown  in  Fig.  3,  which  is  a  pier  for  a  100-foot  span. 


135—28 


8 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


£ fe ration  of  Bait. 


/■Bridge  Seat 


5  X/5 


I 

I 

<t) 


The  distance  from  the  rail  to  the  ground  is  given  as  80  feet; 
that  from  the  rail  to  the  bridge  seat  is  one-fifth  the  span,  or, 

in  this  case,  20  feet.  This 
makes  the  pier  60  feet  high 
from  the  bridge  seat  to  the 
ground  surface.  The  re¬ 
quired  size  of  bridge  seat 
for  this  span  is  given  in 
Art.  14  as  5  ft.  X  15  ft.; 
with  a  batter  of  1  inch  per 
foot,  the  cross-section  of 
the  pier  increases  1  foot 
in  each  direction  for  every 
6  feet  of  height,  which 
makes  15  ft.  X  25  ft.  at 
the  ground  surface.  The 
prismoidal  formula,  given 
in  Geometry ,  Part  2,  is 
best  adapted  to  the  com¬ 
putation  of  the  volume. 
The  cross-section  of  the 
pier  half  way  between 
the  bridge  seat  and  the 
ground  surface  is  10  ft. 
X  20  ft.,  and  the  volume 
of  this  part  of  the  pier  is 


<o 


-/oxzo- 


§ 


/5  X  25 


/  7  X  27 


"O 

L 


G round 
Surface 


found  to  be 


Fig.  3 

60 


[(5  X  15)  +  (4  X  10  X  20)  +  (15  X  25)] 


6  X  27 

=  463  cubic  yards.  The  foundation  is  made  1  foot  larger 
all  around  than  the  bottom  of  the  pier  at  the  ground  surface. 
This  makes  the  base  17  ft.  X  27  ft.  in  cross-section.  If  the 
depth  is  taken  as  5  feet,  the  volume  of  this  part  of  the  pier  is 
5  X  17  X  27 


27 


=  85  cubic  yards.  The  total  volume  of  masonry 


is,  then,  463  -f  85  =  548  cubic  yards.  The  amount  of  exca¬ 
vation,  given  in  the  fourth  column  of  the  table,  is  assumed  to 
be  the  same  as  the  volume  of  the  foundation,  or,  in  this  case, 
85  cubic  yards. 


9 


§  82  BRIDGE  PIERS  AND  ABUTMENTS 

The  total  cost  per  pier,  given  in  the  sixth  column,  bears  no 
relation  to  the  length  of  span,  but  increases  and  then  decreases 
as  the  span  increases.  This  is  because,  in  this  example,  the 
height  of  pier  is  less  for  the  longer  spans,  since  the  bridge 
seat  is  taken  at  a  distance  of  one-fifth  the  span  below  the 
rail.  On  the  other  hand,  the  cost  of  substructure,/^  linear 
foot  of  bridge ,  decreases  rapidly  as  the  span  increases,  so  that 
if  this  were  the  only  consideration,  long  spans  would  be 
desirable.  This  decrease  is  offset,  however,  by  the  increase, 
per  linear  foot  of  bridge ,  of  the  cost  of  the  superstructure. 

19.  Final  Calculation. — From  an  inspection  of  the 
table  in  Art.  17  it  is  seen  that,  on  the  basis  assumed,  the 
cost  of  one  unit  of  substructure  will  equal  the  cost  of  one 
unit  of  superstructure  when  the  length  of  span  is  about 
80  feet,  and  the  cost  per  foot  of  substructure  and  superstruc¬ 
ture  will  be  about  $68.  This  condition  would  call  for  twelve 
or  thirteen  spans,  a  number  that  is  approximately  right;  but,  on 
account  of  the  magnitude  of  the  work,  it  is  advisable  to  carry 
the  computations  further  with  about  this  number  and  length  of 
spans,  using  the  actual  profile  of  the  ground  at  the  crossing 
and  considering  in  detail  the  depth  of  each  pier,  including 
the  foundation.  This  is  necessary  because  the  piers  near  the 
ends  of  the  bridge  will  probably  not  be  so  high  as  those 
near  the  center,  where  the  valley  is  the  lowest.  The  first 
rough  calculation  indicates  about  what  number  of  spans 
should  be  considered;  in  the  second,  more  detailed  calculation. 

20.  Plans. — Unlike  some  other  classes  of  structures,  of 
which  a  great  many  may  be  built  substantially  alike  and  from 
the  same  plans,  it  is  generally  necessary  to  make  a  special 
design  for  every  pier  or  abutment;  for  the  dimensions  and 
shape  of  these  structures  depend  largely  on  greatly  varying 
local  conditions.  It  is  customary  in  all  cases  to  give  the 
general  dimensions,  such  as  height,  width,  length,  etc.  In 
many  cases,  the  sizes  of  stones  to  be  used  are  marked  on  the 
plans,  but  it  is  considered  better  practice  to  allow  the  con¬ 
tractor  to  take  care  of  this  matter.  It  is  sufficient  in  most 
cases  to  specify  the  limiting  sizes  that  will  be  permitted. 


10 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


PIER  DESIGN 


PRACTICAL  CONSIDERATIONS 

21.  Bridge  Seat. — In  designing  a  bridge  pier,  the  first 
matter  to  be  considered  is  the  area  and  plan  of  its  top,  so  as 
to  provide  proper  support  for  the  superstructure.  If  the 
bridge  is  so  designed  that  all  the  bearings  on  the  masonry 
are  at  the  same  elevation,  the  top  of  the  pier  is  made  level 
throughout  its  whole  area. 

The  width  of  the  top  of  a  pier  can  seldom  be  made  less 
than  4  feet,  and  can  be  made  as  narrow  as  this  only  when 
the  adjacent  spans  are  very  short.  This  width  is  necessary 
on  account  of  the  fact  that  the  girders  or  trusses  that  form 
two  adjacent  spans  are  in  the  same  line,  and  sufficient  width 
must  be  provided  to  permit  each  to  have  sufficient  bearing 
surface.  The  nearest  edge  of  the  bearing  plates  should  not 
be  allowed  to  come  closer  than  about  3  inches  to  the  neat 
line  of  the  masonry  under  the  bridge  seat,  and  the  edges  at 
the  ends  of  the  adjacent  spans  should  be  from  6  to  12  inches 
apart.  The  bearing  plates  for  the  shortest  spans  that  usually 
rest  on  piers  can  seldom  be  made  less  than  18  inches  in 
length,  so  it  can  be  readily  seen  that  a  width  of  4  feet  is  as 
small  as  can  be  used.  Allowing  for  an  overhang  of  3  inches 
on  each  side  makes  the  bridge-seat  course  4  feet  6  inches  in 
width.  When  the  bridge  is  on  a  skew,  it  is  necessary  to 
make  the  bridge  seat  somewhat  wider,  in  order  to  keep  the 
bearing  plates  from  coming  too  close  to  the  edges.  Fig.  4 
shows  the  bridge  seat  of  a  pier  and  the  ends  of  two  adjacent 
trusses. 

22.  In  the  length  of  a  pier,  a  more  liberal  allowance  is 
generally  made  than  in  the  width,  the  ends  of  the  pier  being 
carried  from  once  to 'twice  the  width  beyond  the  centers 


11 


§82  BRIDGE  PIERS  AND  ABUTMENTS 


Fig. 


12 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


of  the  outside  trusses  or  girders,  unless  special  conditions 
render  it  necessary  to  adopt  a  smaller  length.  The  extra 
length  at  the  ends  is  considered  necessary  because  it  is  not 
advisable  to  have  an  edge  of  the  masonry  close  to  two  sides 
of  a  bearing  plate;  otherwise,  a  corner  of  the  masonry  may 
break  off  and  allow  the  end  of  the  bridge  to  fall.  The 
increase  is  made  in  the  length  rather  than  in  the  width, 
because  the  former  adds  less  to  the  total  volume  and  cost 
of  the  pier,  and  also  because  it  causes  less  obstruction  under 
the  bridge. 

23.  Pedestal  Blocks. — When  the  design  of  the  bridge 
is  such  as  to  require  supports  at  different  elevations  for 
different  parts  of  the  superstructure,  the  top  of  the  bridge- 
seat  course  is  generally  placed  at  the  elevation  required  for 
the  lowest  supports,  and  the  higher  elevations  are  obtained 
by  placing  stones  or  castings  on  top  of  the  bridge  seat,  or 
by  using  stones  of  different  thicknesses  in  the  bridge-seat 
course.  Fig.  5  shows  three  ways  of  accomplishing  this. 
In  ( a )  and  (c)  stones  of  different  thicknesses  are  placed  on 
top  of  the  bridge  seat,  while  in  (b)  different  thicknesses  are 
used  in  the  bridge-seat  course. 

24.  Batter. — Sufficient  batter  for  the  sides  and  ends  of 
the  pier  should  always  be  provided  for  in  the  design, 
whether  or  not  the  theoretical  conditions  require  the  base 
to  be  greater  than  the  top.  The  batter  usually  starts  at 
the  neat  line  under  the  bridge-seat  course  and  continues 
unbroken  down  to  the  top  of  the  footing  course.  In  ordinary 
practice,  a  batter  of  i  to  li  inches  to  the  foot  is  usually  con¬ 
sidered  sufficient.  When  the  horizontal  cross-section  of  the 
pier  is  rectangular,  the  ends  are  given  the  same  batter  as  the 
sides.  When  there  are  cutwaters,  different  batters  are  used. 

25.  There  are  two  reasons  for  giving  the  pier  a  batter 
on  all  sides:  first,  it  is  usually  required  in  order  to  give  the 
proper  size  of  base;  second,  the  appearance  is  greatly 
improved  by  the  batter.  If  the  sides  were  built  vertical, 
the  pier  would  seem  to  the  eye  to  be  narrower  and  shorter 
at  the  bottom  than  at  the  top. 


$  82 


BRIDGE  PIERS  AND  ABUTMENTS 


13 


26.  Footings. — The  base  or  footing  of  a  pier  should 
always  be  carried  to  such  a  depth  that  it  will  be  safe  from  the 
dangers  of  frost  and  other  surface  disturbances,  and  should 
be  well  protected  from  the  danger  of  undermining,  if  run- 


(C) 

Fig.  5 


ning  water  is  near.  The  footing  must  be  of  sufficient  size 
to  properly  distribute  the  load  without  exceeding  the  safe¬ 
bearing  power  of  the  subfoundation.  When  only  practical 
conditions  govern  the  size  of  the  pier,  the  batter  is  usually 
continued  unbroken  to  the  surface  of  the  ground.  The  sides 


14  BRIDGE  PIERS  AND  ABUTMENTS  §  S2 

\ 

and  ends  are  then  stepped  out  or  offset  6  inches  or  1  foot  to 
form  the  footing,  and  the  sides  are  continued  vertical  down¬ 
wards  to  the  subfoundation. 

27.  Heiglit  of  Pier. — It  is  very  important  that  the  top 
of  a  pier  be  brought  to  the  proper  height.  For  bridges  over 
city  streets,  the  height  is  usually  controlled  by  the  required 
amount  of  headroom  beneath.  When  a  pier  is  to  be  placed 
in  running  water,  special  care  must  be  taken  to  study  all  the 
conditions.  The  highest  point  to  which  the  water  has  ever 
reached  must  be  ascertained,  and  the  top  of  the  pier  placed 
well  above  it.  In  addition,  it  must  be  borne  in  mind  that  the 
pier  will  be  an  obstruction  in  the  stream;  on  this  account,  ice 
or  drift  may  collect  to  a  height  of  several  feet,  causing  the 
water  to  rise  higher  than  it  did  before.  The  steelwork  of 
the  bridge  should  be  placed  so  high  that  it  will  never  be  in 
danger  of  being  knocked  off  the  pier  by  blows  from  the  ice 
or  drift.  Even  where  there  is  no  current,  the  top  of  the  pier 
should  be  placed  so  high  that  the  steelwork  of  the  bridge 
will  not  be  subject  to  corrosion  on  account  of  contact  with 
the  water. 

28.  Piers  in  Streets  and  Highways. — Usually,  when 
a  bridge  crosses  a  body  of  water,  the  piers  are  carried  up 
high  enough  for  the  bridge  to  rest  directly  on  them.  In 
many  other  cases,  however,  the  piers  are  carried  only  a 
short  distance  above  the  surface  of  the  ground,  and  the 
bridge  is  supported  by  columns  that  rest  on  the  piers. 
This  is  the  case  in  many  railroad  bridges  over  city  streets 
and  highways.  The  abolition  of  grade  crossings  of  high¬ 
ways  with  railroads  calls  for  a  great  number  of  bridges,  and 
many  of  these  have  low  piers.  When  the  street  or  highway 
is  wide,  it  is  found  more  economical  to  use  several  short 
spans  than  one  long  span.  A  pier  is  placed  at  the  center  of 
the  street,  or  at  each  curb  line,  or  at  both  the  center  and  the 
curb  lines.  Then,  since  the  piers  would  take  up  so  much  of 
the  width  of  the  street,  only  the  footings  are  built,  and  the 
columns,  which  occupy  much  less  width,  are  placed  directly 
on  the  footings.  In  this  case,  the  base  of  each  column 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


15 


should  be  covered  with  concrete  to  such  a  width  that  wheels 
of  passing  vehicles  cannot  hit  the  columns,  and  also  to  pro¬ 
tect  the  bases  of  the  columns  from  the  corrosion  that  might 
be  caused  by  the  collection  of  dirt  and  moisture.  The  low 
piers  that  support  the  columns  are  for  the  purpose  of  spread¬ 
ing  the  loads  evenly  over  the  proper  area  of  subfoundation. 


Top  of  Coping  fo  be  Bushhammereef 
io  a  True  and  Lerei  Surface. 


It  should  be  kept  in  mind  that  piers  built  in  city  streets 
in  which  there  is  much  traffic  will  be  very  conspicuous  if 
carried  up  to  the  bridge,  and  the  designer  should  attempt 
to  make  them  look  as  artistic  as  practicable.  A  very  simple 
way  to  improve  the  appearance  is  to  point  or  round  the  ends. 
Fig.  6  gives  dimensions  for  a  pier  reaching  up  to  the  bridge 


1(3 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


for  a  single-track  railroad  bridge  suitable  for  location  in  a 
street.  Fig.  7  gives  the  dimensions  for  a  low  pier  for  the 
support  of  columns  or  trestle  bents. 

29.  Piers  Near  Railroad  Tracks.  —  In  the  case  of 
bridges  over  railroad  tracks,  it  is  often  necessary  or  advis¬ 
able  to  provide  supports  near  the  tracks  below.  Many  engi¬ 
neers  provide  these  supports  by  means  of  steel  trestles 
resting  on  low  masonry  piers  similar  to  that  shown  in 
Fig.  7.  When  columns  are  used,  it  is  not  advisable  to  have 
them  extend  down  to  the  track  level,  for  a  derailed  train 
might  run  into  them  and  cause  the  bridge  to  fall.  In  order 


to  avoid  all  possibility  of  such  an  accident,  it  is  advisable  to 
have  the  masonry  extend  up  to  about  10  feet  above  the 
track,  so  that  in  case  of  a  derailment  the  masonry  pier  can 
resist  the  shock.  Of  course,  it  is  a  serious  matter  for  a 
derailed  train  to  strike  a  masonry  pier,  but  it  would  be  still 
more  serious  for  it  to  knock  the  supports  out  from  under  a 
bridge,  causing  the  latter  to  fall  on  and  crush  the  train. 
For  similar  reasons,  the  masonry  work  of  piers  in  navigable 
streams  should  be  made  of  sufficient  height  to  protect  the 
bridge. 

30.  Piers  for  Trestles. — For  high  trestles  over  land, 
long  spans  are  sometimes  used,  and  then  the  piers  are 
continued  up  to  the  bottom  of  the  bridge.  In  the  majority 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


17 


of  cases,  however,  shorter  spans  are  used,  and  it  is  found  to 
be  more  economical  to  have  the  pier  extend  only  a  short 
distance  above  the  surface  of  the  ground,  and  to  support  the 
bridge  by  means  of  a  steel  tower  resting  on  the  pier.  For 
low  trestles,  the  pier  is  usually  made  continuous  across  the 
track,  so  that  it  will  support  two  or  more  of  the  columns 
that  compose  the  trestle  bent.  The  pier  shown  in  Fig.  7  is 
suitable  for  such  conditions,  the  length  depending  on  the 
length  of  the  bent. 

31.  Pedestals  for  High  Trestles. — High  trestles  are 
generally  built  with  short  tower  spans  of  from  30  to  50 


P  1 

3  C 

Fig.  8 

feet,  alternating  with  longer  spans,  as  shown  in  Fig.  8.  The 
trestle  bents  that  form  the  towers  are  placed  in  vertical 
planes,  as  shown  at  ( a ),  but  the  outside  columns  in  the  bent 
(there  are  usually  but  two)  are  inclined  outwards  from  the 
track,  with  a  batter  of  li  to  3  inches  per  foot,  as  shown 
at  ( b ).  For  high  trestles,  this  calls  for  supports  at  such 
distances  apart  that  it  is  generally  undesirable  to  make  a 

t 

continuous  pier  for  each  bent.  A  separate  masonry  support, 
usually  called  a  pedestal,  is  then  provided  for  each  column. 
These  pedestals  should  extend  far  enough  into  the  ground 
to  be  able  to  resist  the  action  of  frost  and  other  destructive 
surface  agents,  and  their  bases  should  be  made  large  enough 


18 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


to  eliminate  any  possibility  of  settling.  The  horizontal  dis¬ 
tance  between  the  pedestals  at  the  base  of  a  tower  is  generally 
much  less  than  the  distance  from  the  top  of  the  pedestals  to 
the  track.  On  this  account,  whenever  one  pedestal  settles, 
the  track  above  is  thrown  out  of  line  a  greater  amount  than 
the  amount  of  the  settlement,  and  one  rail  sinks  below  the 
other.  If  the  tower  above  is  very  strongly  braced,  both  hori¬ 
zontally  and  diagonally,  as  is  customary  in  the  best  practice, 
one  of  the  pedestals  can  settle  without  causing  the  column 
above  it  to  settle,  this  columil  being  held  up  by  the  bracing 
while  there  is  no  load  on  the  bridge.  As  soon  as  sufficient 
load  comes  on  the  column,  however,  the  latter  will  be  forced 
down  on  top  of  the  pedestal,  and,  in  the  case  of  a  railroad 
bridge,  the  train  may  be  thrown  off  the  trestle.  It  is  thus  seen 
that  it  is  of  the  utmost  importance  to  provide  a  sufficient  area 
of  base  for  pedestals,  especially  for  high  trestles,  and  also  to 
provide  proper  foundations.  The  possible  result  of  settle¬ 
ment  here  is  much  greater  than  in  the  case  of  continuous 
piers  under  low  bridges.  In  addition,  if  any  settlement  should 
occur,  it  will  be  a  very  difficult  matter  to  rectify.  The  out¬ 
lines  of  several  pedestals  showing  the  customary  method  of 
spreading  the  courses  over  a  greater  base  are  shown  in  Fig.  8. 

32.  As  a  rule,  trestle  bents  are  so  designed  that,  although 
the  columns  are  inclined  outwards,  the  load  on  each  pier  will 
be  vertical,  except  in  case  of  wind.  •  The  outward  thrust  is 
usually  resisted  by  the  horizontal  bracing  of  the  bent.  For 
this  reason,  the  center  lines  of  the  pedestals  are  vertical.  For 
pedestals  on  a  side  hill,  allowance  for  the  tendency  of  the 
pedestals  to  overturn  or  slide  downwards  must  be  considered 
and  the  foundations  placed  lower.  As  a  rule,  this  tendency 
can  be  overcome  by  making  the  pedestals  several  feet  deeper 
than  those  on  level  ground.  On  a  side  hill,  care  must 
also  be  taken  to  make  the  tops  of  the  piers  high  enough  to 
keep  clear  of  the  earth  that  may  roll  down,  and  to  keep  the 
steel  or  wooden  posts  out  of  the  dirt  at  all  times;  otherwise, 
it  is  desirable  to  keep  the  tops  of  the  pedestals  as  low  as 
possible. 


20  BRIDGE  PIERS  AND  ABUTMENTS  §  82 

33.  Piers  for  Running  Streams. — Outlines  of  piers 
suitable  for  running  stream  are  shown  in  Figs.  9,  10,  and 
11  for  moderate  heights,  and  in  Fig.  12  for  a  long  span  bridge 
over  a  deep  river.  It  will  be  noticed  that  in  Fig.  12  the  bat¬ 
ter  of  the  sides  of  the  pier  is  smaller  than  usual.  The  batter 
is  frequently  decreased  for  a  large  pier;  for,  at  best,  it  is  a 
serious  obstruction  to  the  flow  of  the  water,  and  it  is  desir¬ 
able  to  reduce  the  amount  of  obstruction  as  much  as  possible. 
A  small  batter  can  be  used  only  for  a  pier  under  a  long  span. 


In  such  a  case,  it  is  necessary  to  provide  a  large  bridge  seat, 
the  width  of  which  is  often  sufficient  for  the  foundation.  A 
small  batter  is  provided,  however,  for  the  sake  of  appearance. 
The  stability  of  such  a  high  pier  is  a  subject  for  careful  study, 
as  will  be  described  presently.  It  may  be  remarked  here, 
however,  that  in  a  pier  under  a  long  span,  the  dead  weight 
is  so  great  that  the  pier  is  usually  safe  against  any  overturn¬ 
ing  forces  to  which  it  is  likely  to  be  subjected. 

.  34.  Nosings  or  Cutwaters. — The  form  of  nosing 
usually  adopted  for  a  pier  in  running  water  is  the  result  of  a 
compromise  between  the  form  that  would  reduce  the  eddies 


(a) 


-30-0" - 

(C) 


21 


22 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


Center  L/ne  of  Pier, 


Fig.  13 


Center  L/ne  of  P/er 


and  whirlpools  to  a  minimum,  and  the  modifications  of  that 
form  which  permanency  and  economy  demand.  To  reduce 
the  obstruction  to  the  current  to  a  minimum,  the  ends  of  the 
pier  should  be  provided  with  nosings  pointed  gently  by  means 
of  a  reversed  curve,  as  shown  in  Fig.  13.  This  form,  how¬ 
ever,  would  involve  expensive  stone  cutting  or  concrete  forms, 

and  is  seldom  used. 
A  simpler  form ,  which 
is  almost  as  efficient 
in  turning  aside  the 
water,  consists  in  con¬ 
tinuing  the  long  sides 
by  curved  surfaces 
until  they  meet  in  a 
line,  as  shown  in  out¬ 
line  in  Fig.  14.  This 
form  is  the  best  for 
large  piers,  from  the 
standpoint  of  both 
durability  and  ex¬ 
pense,  and  is  shown 
on  the  lower  part  of 
the  pier  in  Fig.  12.  In  the  common  form  for  ordinary  piers, 
the  end  is  pointed  by  two  plane  surfaces  coming  together,  as 
shown  in  outline  in  Fig.  15,  and  also  in  Figs.  9  and  10.  The 
planes  forming  the  nosing  should  make  angles  of  from  30°  to 
60°  with  the  center  line  of  the  pier.  An  angle  of  45°  with 
the  center  line,  making  the  point  90°,  as  shown  in  Fig.  15,  is 
frequently  used. 


T”  ~  ^ 

Fig.  14 

(  Center  L  /ne  of  P/'er 

\h 

O'  \ 

C\  \ 

) 

o>  / 

- ^ — r 

Fig.  15 


35.  At  the  down-stream  end,  the  two  planes  that  come 
together  are  given  the  same  batter  as  the  sides.  In  cold 
regions,  where  much  ice  may  be  expected,  the  nosing  at  the 
up-stream  end  of  the  pier  is  given  a  greater  batter,  so  that 
the  slope  of  the  nose  will  incline  at  the  rate  of  3  to  6  inches 
per  foot.  The  sharp  edge  is  frequently  shod  with  iron,  which 
acts  as  an  ice  breaker.  The  momentum  of  the  moving  ice 
and  the  pressure  from  the  current  of  water  force  the  cakes 


BRIDGE  PIERS  AND  ABUTMENTS 


§  82 


23 


of  ice  to  slide  up  this  smooth  edge;  when  high  enough  out 
of  the  water,  the  ice  breaks  of  its  own  weight,  or  by  the 
blows  of  other  ice  forced  against  it. 

The  increased  cost  of  curved  ends  on  large  piers  is  very 
small,  and  since  the  obstruction  to  the  water  is  large,  it  is 
customary  in  practice  to  curve  the  ends,  as  previously  shown 
in  Fig.  12.  If  the  ends  were  given  the  theoretically  proper 
form  shown  in  Fig.  13,  the  sharp  point  would  soon  be  worn 
away.  Semicircular  ends  are  sometimes  used;  but,  if  there 
is  much  current,  bad  eddies  and  whirlpools  result,  and  there 
is  danger  of  the  water  being  so  agitated  as  to  undermine 
the  pier. 

When  the  pier  does  not  extend  more  than  10  or  15  feet 
above  the  high-water  line,  it  is  customary  to  have  the  cut¬ 
water  extend  up  to  the  bottom  of  the  bridge-seat  course,  as 
shown  in  Fig.  9.  In  very  high  piers,  in  which  this  procedure 
would  involve  much  needless  expense,  the  nosings  are  usually 
carried  but  a  few  feet  above  high-water  mark,  and  the 
remainder  of  the  pier  is  made  with  square  ends,  as  shown 
in  Figs.  10  and  11.  When  it  is  desired  to  give  high  piers  a 
better  appearance,  the  ends  of  the  upper  part  may  be  made 
semicircular,  as  shown  in  Fig.  12. 

36.  Belt  Course. — In  case  the  upper  part  of  the  pier  is 
arranged  differently  from  the  lower,  they  are  separated  from 
each  other  by  means  of  a  belt  course,  similar  to  a  bridge- 
seat  course.  The  belt  course  is  indicated  by  the  letters  A ,  A 
in  Figs.  11  and  12. 

-  , 

THEORETICAL  CONDITIONS 

37.  After  the  approximate  dimensions  of  a  pier  have 
been  decided  according  to  the  foregoing  practical  considera¬ 
tions,  it  is  necessary  to  investigate  the  stability  of  the  pier 
and  to  make  all  the  calculations  necessary  to  determine 
whether  the  actual  stresses  will  anywhere  exceed  the  allow¬ 
able  stresses. 


135— 29 


24 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


CAUSES  OF  FAILURE 

38.  The  stability  of  a  bridge  pier  may  be  destroyed  by 
any  one  of  the  following  causes: 

1.  Overturning  at  any  section  or  on  the  subfoundation  on 
account  of:  (a)  pressure  of  the  wind  on  the  structure  and 
on  the  loads  carried  by  the  structure;  ( b )  the  current  in  the 
stream,  and  the  pressure  and  blows  from  ice  and  other  float¬ 
ing  objects;  (c)  the  centrifugal  force  of  trains;  and  ( d )  the 
longitudinal  thrust  due  either  to  the  friction  of  the  wheels  on 
the  rails  when  brakes  are  set,  or  to  the  traction  of  the  engine. 

2.  Sliding  at  any  cross-section  or  on  the  subfoundation. 

3.  Crushing ,  either  at  the  bridge  seat,  at  any  lower 
section,  or  at  the  base. 

4.  Failure  of  the  foundation  or  sub  foundation,  either  from 
insufficient  strength,  from  the  upheaval  by  frost,  or  from 
other  disturbing  agents. 

5.  Breaking  apart  or  collapsing,  on  account  of  poor  mortar, 
poor  bond  between  the  stones,  or  poor  concrete. 

39.  Overturning. — In  a  direction  parallel  to  the  axis 
of  the  bridge,  the  forces  tending  to  overturn  the  pier  are  the 
pressure  of  the  wind,  the  longitudinal  thrust  from  trains  in 
railroad  bridges,  and  the  packing  of  ice  or  drift  between  the 
piers  or  between  a  pier  and  the  bank  of  a  stream.  In  case 
the  earth  extends  to  a  greater  height  on  one  side  of  a  pier 
than  on  the  other,  the  unbalanced  pressure  must  not  be 
overlooked.  These  forces  act  to  overturn  the  pier  in  the 
direction  of  its  smallest  dimension  and  least  resistance. 

In  a  direction  at  right  angles  to  the  axis  of  bridge,  there 
may  be  a  pressure  of  the  wind  not  only  on  the  pier  but  also 
on  the  bridge  and  on  the  train  or  other  load,  and  the 
force  of  the  current  may  be  added  to  the  pressure  of  the  ice 
and  drift;  there  may  also  be  centrifugal  force  if  the  track  is 
on  a  curve.  The  centrifugal  force  can  act  only  toward  the 
outside  of  the  curve,  and  the  force  of  the  current  can  act 
only  in  the  direction  of  the  flow;  but  the  other  forces  may 
be  exerted  in  either  direction. 


§82  BRIDGE  PIERS  AND  ABUTMENTS  25  • 

Although  the  overturning  forces  acting  on  a  pier  are  dif¬ 
ferent  in  their  origin  from  the  pressure  of  a  bank,  their 
effects  and  the  necessary  dimensions  to  resist  them  are 
determined  in  the  same  way  as  for  retaining  walls,  and  here 
it  will  be  sufficient  to  make  a  few  general  remarks  as  to 
their  character  and  magnitude. 

40.  With  a  low  pier,  or  with  one  of  moderate  height, 
the  dimensions  required  for  supporting  the  bridge  are  such 
that  there  is  little  danger  of  overturning;  but  with  a  very  high 
pier,  the  overturning  forces  should  be  carefully  looked  into 
and  provision  made  to  resist  them. 

A  pier  will  never  overturn  about  a  sharp  edge,  unless  the 
sharp  edge  crushes  or  sinks  into  the  soil.  This  must  be 
prevented  by  so  designing  the  pier  that  the  safe  crushing 
strength  of  the  masonry  and  the  safe  bearing  power  of  the 
soil  will  not  be  exceeded.  Since  the  maximum  force  of  the 
wind  and  of  the  longitudinal  thrust  are  of  rare  occurrence 
and  of  brief  duration,  the  intensities  of  pressure  usually 
permitted  may  be  increased  25  per  cent,  when  these  over¬ 
turning  forces  are  considered  as  acting  at  the  same  time. 

In  the  Section  on  Foundatio?is ,  Part  1,  may  be  found  tables 
giving  the  safe  bearing  power  of  various  soils  and  the  safe 
crushing  stresses  for  masonry. 

41.  Sliding. — The  forces  tending  to  produce  sliding  of 
a  pier  on  its  subfoundation,  or  along  any  horizontal  plane 
within  the  pier,  are  the  same  as  those  that  tend  to  overturn 
it.  The  method  of  determining  the  effect  of  these  forces 
and  of  providing  for  them  is  the  same  as  for  retaining  walls. 

42.  Crushing. — The  weight  of  the  bridge  and  its  load 
is  usually  transmitted  to  the  pier  at  two  or  more  points  so 
far  apart  that,  if  ample  provision  is  made  for  distributing  this 
load  over  a  sufficient  area  at  the  bridge  seat,  there  need  be 
no  fear  that  crushing  at  any  lower  plane  in  the  masonry  may 
be  caused  by  that  weight.  The  only  surfaces  that  heed  be 
considered  are  the  bridge  seat,  the  bottom  of  the  pier,  where 
it  rests  on  the  footing,  and  the  base  of  the  footing.  The 
overturning  forces  cause  the  center  of  pressure  to  fall  near 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


26 

the  edge  of  the  masonry,  and  the  danger  of  crushing  from 
this  cause  must  be  carefully  investigated. 

43.  Crushing'  at  Bridge  Seat. — In  determining  the  area 
of  bearing  of  the  bridge  on  the  masonry,  it  should  be  borne 
in  mind  that  the  load  is  not  generally  uniformly  distributed 
over  the  whole  area  of  bearing;  even  with  a  perfectly  rigid 
bearing  plate  there  may  be  a  greater  load  on  one  edge  than 
on  another,  on  account  of  the  deflection  of  the  bridge  under 
its  load,  or  on  account  of  the  overturning  forces.  Since  it  is 
impossible  to  compute  the  actual  distribution  of  the  pressure, 
it  is  customary  to  take  into  account  only  the  vertical  loads 
and  to  use  a  much  smaller  working  stress  than  would  be 
justifiable  if  the  uneven  distribution  could  be  properly  taken 
into  account.  On  this  basis,  a  working  pressure  of  about 
300  pounds  per  square  inch  is  commonly  used  for  limestone 
or  sandstone,  400  for  concrete,  and  500  for  granite.  This 
gives  an  apparent  factor  of  safety  of  about  10  or  more. 

44.  Crushing  at  Bower  Sections. — In  considering  the 
crushing  strength  of  a  pier  at  any  horizontal  plane  below 
the  bridge  seat,  it  is  necessary  to  take  into  account  the 
uneven  pressure  due  to  the  overturning  forces.  The  prin¬ 
ciples  involved,  including  the  rule  of  the  middle  third,  are 
fully  explained  in  Foundations ,  Part  1;  how  they  are  applied 
will  be  illustrated  by  an  example  to  be  given  presently. 

Crushing  of  the  masonry  at  special  places  may  also  be 
caused  by  other  agents  than  the  forces  heretofore  considered, 
as  by  blows  from  the  wheels  of  vehicles,  from  vessels,  ice, 
etc.  These  causes  of  destruction  or  damage  will  be  taken 
up  in  a  subsequent  article. 

45.  Failure  of  Foundation. — The  most  frequent  cause 
of  failure  of  a  bridge  pier  or  abutment  is  a  poor  foundation, 
which  may  either  crush  entirely  under  the  load  so  as  to  cause 
a  settlement  of  the  structure,  or  yield  slightly  at  the  point  of 
maximum  pressure,  and  so  increase  the  already  excessive 
overturning  tendency  by  decreasing  the  leverage  of  the 
vertical  forces  and  thus  decreasing  the  resisting  moment. 
The  subfoundation,  by  its  lack  of  uniformity,  may  cause 


BRIDGE  BIERS  AND  ABUTMENTS 


27  . 


uneven  settlement  and  the  rupture  of  the  'masonry.  The 
upheaving  tendency  of  frost  is  also  a  disturbing  agent.  A 
subfoundation  that  may  have  enough  resistance  to  support 
the  load  may  fail  by  being  softened  or  washed  away  by  the 
current,  if  in  a  running  stream.  A  flood  may  sometimes 
cause  the  undermining  of  a  structure  that  at  ordinary  stages 
of  the  water  is  far  away  from  the  water. 


FORCES  TO  BE  RESISTED 

46.  Wind. — In  the  design  of  a  bridge  and  its  supports, 
it  is  customary  to  provide  for  a  wind  pressure  of  50  pounds 
per  square  foot  of  exposed  surface  when  there  are  no  loads 
on  the  bridge,  or  an  alternative  pressure  (for  railroad  bridges 
only)  of  30  pounds  per  square  foot  on  the  exposed  surface 
of  the  bridge  and  the  loads  combined  when  there  are  loads 
on  the  bridge.  '  The  pressure  of  50  pounds  per  square  foot 
corresponds  to  a  velocity  of  over  100  miles  per  hour,' and  is 
equivalent  to  a  hurricane  that  would  be  commonly  reported 
as  “destroying  everything  in  its  path.”  Such  wind  is  of 
extremely  rare  occurrence,  but  since  it  may  occur  at  any 
time,  even  if  for  a  very  short  time  only,  it  must  be  provided 
for.  The  alternative  pressure  of  30  pounds  per  square  foot 

i 

corresponds  to  a  velocity  of  over  80  miles  per  hour,  and  is 
the  greatest  pressure  considered  on  moving  loads,  such  as 
railroad  cars,  since  it  is  sufficient  to  overturn  empty  cars; 
and  it  is  assumed  in  practice  that  if  the  wind  blows  harder 
than  this,  it  will  be  impossible  to  operate  cars  or  other  vehi¬ 
cles,  so  that  there  will  probably  be  no  loads  on  the  bridge. 

In  determining  the  total  pressure  on  a  bridge,  the  intensity 
is  multiplied  by  the  exposed  area.  This  area  is  usually  taken 
equal  to  the  area  of  the  longitudinal  vertical  projection  of  the 
bridge,  and  is  found  by  multiplying  the  width  of  each  mem¬ 
ber  by  its  length;  in  a  truss  bridge,  the  sum  of  the  areas  of 
all  the  trusses  should  be  taken.  In  the  design  of  highway 
bridges,  the  exposed  area  of  the  loads  is  usually  very  small 
in  comparison  with  the  exposed  area  of  the  bridge,  and  it  is 
customary  to  neglect  it.  In  railroad  bridges,  the  cars  present 


28 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


a  vertical  surface  about  10  feet  high  and  for  the  full  length  of 
an  ordinary  bridge.  This  gives  30  X  10,  or  300,  pounds  per 
linear  foot  wind  pressure  on  a  train  of  cars.  For  purposes 
of  computation,  this  pressure  is  treated  as  a  single  force 
acting  through  the  center  of  pressure,  which  is  from  6  to 
9  feet  above  the  rail.  In  what  follows,  the  center  of  pres¬ 
sure  will  be  assumed  to  be  7  feet  above  the  top  of  the  rail. 

47.  Current  of  Stream. — The  pressure  of  the  water  in 
a  flowing  stream  is  given  by  the  following  approximate 
formula: 

p  =  it®!  =  2.96  V\  (1) 

O 

in  which  p  —  pressure,  in  pounds  per  square  foot,  of  exposed 

surface  normal  to  the  current; 
v  =  velocity  of  current,  in  feet  per  second; 

V  =  velocity  of  current,  in  miles  per  hour. 

The  velocity  of  the  current  varies  with  the  depth,  being 
greatest  near  the  surface  and  much  less  at  the  bottom  of  the 
stream.  Between  these  depths  it  varies  approximately  as 
the  square  root  of  the  distance  from  the  bottom.  This  makes 
the  intensity  of  pressure  due  to  the  current  vary  approxi¬ 
mately  as  the  distance  from  the  bottom,  and  the  average  pres¬ 
sure  is  usually  assumed  as  about  one-half  that  at  the  surface, 
with  the  center  of  pressure  at  two-thirds  the  height  from  the 
bottom  to  the  top  of  the  stream.  In  a  pier  having  a  cutwater 
with  inclined  sides,  the  resistance  to  the  flow  of  the  water, 
and  consequently  the  pressure  at  the  end,  are  reduced.  The 
pressure  on  the  end  of  such  a  pier  is  usually  assumed  to 
be  three-quarters  of  the  pressure  on  a  pier  with  a  square 
end.  For  a  pier  with  a  cutwater,  formula  1  may,  therefore, 
be  written 

p  =  1.03  v2  =  2.22  Xs  (2) 

The  pressure  decreases  from  the  surface  to  the  bed  of  the 
stream  the  same  as  for  a  square-ended  pier. 

Let  p<>  =  intensity  of  pressure  at  surface,  in  pounds  per 
square  foot; 

^ol  ,  .,  t  n  .  r  ■  [feet  per  second; 

t  =  velocity  of  flow  at  surface  in  {  .  ^  ’ 

V0]  I  miles  per  hour; 


BRIDGE  PIERS  AND  ABUTMENTS 


29 


§82 


A  =  area,  in  square  feet,  of  section  of  pier  made  by 
a  plane  perpendicular  to  the  current,  between 
the  surface  and  the  bottom  of  the  stream; 

P  =  total  pressure,  in  pounds,  on  the  submerged 
portion. 

Then,  since  the  average  intensity  of  pressure  is  i p0, 

P=±Ap0  (3) 

The  value  of  p0  is  found  by  substituting  v0  or  V0  in  for¬ 
mula  1  or  in  formula  2,  according  to  the  character  of  the 
end.  Making  the  substitution,  formula  3  becomes,  for 
square-end  piers, 

P  =  .69  A  Vo2  =  1.48  A  V0 2 

or,  practically, 

P  =  .7  A  Vo*  =  1.5  A  Vn3  (4) 

For  piers  with  cutwaters, 

P  =  .52  A  Vo2  =  1.11  A  Vo 

or,  practically, 

P  =  .5  A  Vo*  =  1.1^  Vo 2  (5) 

As  already  stated,  the  center  of  pressure  is  taken  at  a 
distance  from  the  bottom  equal  to  two-thirds  of  the  distance 
between  the  bottom  and  the  surface. 

48.  Ice  and  Drift. — In  cold  climates,  ice,  and  in  all 
climates,  drift,  may  pack  around  the  pier,  and,  by  adhering  to 
it,  present  a  much  wider  obstruction  to  the  current  than  does 
the  pier  alone.  In  some  cases,  a  dam  may  be  formed  by  the 
ice  or  drift  packing  solid  from  pier  to  pier;  the  result  is  that 
the  obstruction  increases,  becoming  higher  and  higher,  until 
the  piers  fall  down  or  the  obstruction  is  forced  through  the 
opening  by  the  pressure  of  the  water.  Damage  may  also 
result  if  large  masses  of  ice  floating  with  high  velocities 
strike  the  pier;  in  this  case,  the  pier  may  be  turned  over  or 
part  of  it  may  be  torn  away.  There  is  also  an  element  of 
danger  in  the  expansion  of  water  when  freezing.  If  the 
entire  surface  of  the  water  between  two  piers  freezes  to  a 
considerable  depth,  there  will  be  a  pressure  on  each  pier, 
which,  under  some  conditions,  may  be  sufficient  to  dislodge 
them. 


:;o 


BRIDGE  PIERS  AND  ABUTMENTS 


8 


The  dangers  outlined  ’in  the  preceding  paragraph  are  real 
dangers  and  should  never  be  ignored  or  minimized  in  the 
design  of  piers.  The  history  of  bridge  failures  and  disasters 
shows  that  more  failures  have  been  due  to  the  collapse  of 
the  piers  on  account  of  ice  and  drift  than  to  any  other  one 
cause.  Owing  to  the  extreme  difficulty  in  obtaining  definite 
information  regarding  the  amount  of  these  forces,  it  is  practi¬ 
cally  impossible  to  give  any  values  that  will  be  of  help  to 
the  designer.  Provision  is  usually  made  by  the  use  of  a 
large  factor  of  safety. 

49.  With  regard  to  the  method  of  providing  against  these 
dangers,  it  may  be  said  that  the  problem  is  one  of  judgment 
rather  than  of  computation.  Each  case  must  be  considered 
by  itself,  and  all  the  conditions  and  possibilities  fully  studied 
before  locating  the  piers.  In  many  cases,  the  danger  from 
ice  and  drift  will  be  the  determining  factor  in  the  location  of 
the  piers,  and  may  result  in  the  selection  of  a  single  span 
over  the  waterway,  in  order  to  keep  the  piers  safe.  In  any 
case,  the  problem  is  rather  one  for  the  experienced  engineer 
than  for  the  draftsman  or  designer.  A  young*  engineer 
should  not  hesitate  to  seek  advice  from  more  experienced 
engineers  when  he  has  a  problem  of  this  kind. 

50.  Centrifugal  Force. — In  railroad  bridges  on  which 
the  track  is  curved,  the  centrifugal  force  A  of  a  train  causes 
an  outward  thrust,  the  magnitude  of  which  is  given  by  the 
formula 

F  -  .00001167  V'D  W,  (1) 

in  which  V  =  velocity  of  train,  in  miles  per  hour; 

D  =  degree  of  curve; 

IV  —  weight  of  train. 

For  practical  work,  the  following  formula  may  be  used 

(see  Bridge  Specifications)'. 

F  =  --4--5  .T_i?_g)  WD  (2) 

100  * 

Formula  2  provides  for  about  61  miles  per  hour  for  a 
1°  curve,  55  miles  per  hour  for  a  5°  curve,  and  46  miles  per 
hour  for  a  10°  curve,  which  are  as  high  speeds  as  usually 


BRIDGE  PIERS  AND  ABUTMENTS 


O  - 


obtain.  The  centrifugal  force  F  is  usually  assumed  to  act 
about  6  feet  above  the  top  of  the  rail. 

51.  Longitudinal  Thrust. — The  longitudinal  thrust  is 
due  to  the  friction  of  the  wheels  on  the  rails.  When  a  loco¬ 
motive  is  on  a  bridge  and  is  exerting  its  maximum  tractive 
force,  the  rails  transmit  an  equal  force  to  the  bridge,  and  the 
latter  transmits  it  to  the  supports.  The  tractive  force  has 
been  found  in  some  cases  to  be  as  high  as  37  per  cent,  of  the 
total  weight  on  the  drivers  of  the  locomotive.  When  the 
brakes  of  a  train  are  set,  the  wheels  tend  to  slide  on  the  rails, 
and  this  causes  a  frictional  force  that  is  transmitted  to  the 
supports.  In  practice,  it  is  customary  to  assume  that  the 
greatest  longitudinal  thrust  that  need  be  provided  for  is  equal 
to  20  per  cent,  of  the  greatest  vertical  load  that  can  come  on 
the  bridge.  The  longitudinal  thrust  is  usually. considered  as 
a  single  horizontal  force  acting  above  the  pier  at  the  height 
of  the  bridge  seat;  it  should  never  be  neglected,  as  it  acts  in 
the  direction  in  which  the  pier  is  weakest. 

The  longitudinal  thrust  is  transmitted  to  the  piers  and 
abutments  of  the  fixed  ends  of  the  spans.  The  expansion 
ends,  especially  of  long  spans,  are  provided  with  rollers,  so 
these  ends  cannot  be  relied  on  to  transmit  any  of  the  thrust. 
For  this  reason,  it  is  necessary  to  consider  the  arrangement 
of  the  spans  and  find  out  which  will  be  expansion  and  which 
fixed  ends.  In  case  two  fixed  ends  come  on  the  same  pier, 
that  pier  must  be  designed  to  provide  for  the  longitudinal 
thrust  coming  from  two  spans. 


ILLUSTRATIVE  EXAMPLE 

52.  Data. — Let  the  pier  shown  in  Fig.  16  support  the 
fixed  ends  of  two  150-foot  spans  of  a  single-track  railroad 
bridge  on  a  tangent.  Let  the  data  be  assumed  as  follows: 

Dimensions  as  given  in  figure,  determined  from  practical 
considerations. 

Weight  of  granite  masonry,  150  pounds  per  cubic  foot. 

Weight  of  bridge,  2,500  pounds  per  linear  foot. 


Fig.  16 


32 


82  BRIDGE  PIERS  AND  ABUTMENTS 


33  . 


Surface  of  each  truss  exposed  to  the  wind,  8  square  feet 
per  linear  foot. 

Surface  of  bridge  floor  exposed  to  the  wind,  4  square  feet 
per  linear  foot. 

Minimum  weight  of  train,  800  pounds  per  linear  foot. 

'  Maximum  weight  of  train,  4,000  pounds  per  linear  foot. 

Velocity  of  the  current  at  the  surface  of  the  water,  6  miles 
per  hour. 

Ice  and  drift  collected  about  the  up-stream  end  of  the  pier 
for  a  depth  of  6  feet  below  high-water  level,  and  for  an 
average  width  of  18  feet. 

It  is  required  to  determine  the  stability  of  the  pier  in 
regard  to  overturning  and  sliding,  and  also  to  find  the 
maximum  intensity  of  pressure  on  the  foundation. 

53.  Overturning. — In  investigating  the  factor  of  safety 
against  overturning,  it  is  necessary  to  consider  overturning 
moments  in  both  directions  of  the  pier;  that  is,  at  right 
angles  and  parallel  to  the  axis  of  the  bridge.  It  is  also 
necessary  to  consider  the  two  conditions  of  a  loaded  and  an 
unloaded  bridge. 

In  discussing  this  subject,  three  cases  will  be  considered. 
In  Case  I,  the  wind  pressure  is  taken  as  30  pounds  per 
square  foot  (see  Art.  46);  in  Case  II,  it  is  taken  as  50  pounds 
per  square  foot.  In  Case  I,  it  is  customary  to  use  the 
weight  of  an  empty  train,  since  the  overturning  moment 
is  then  the  same  as  though  a  full  train  were  considered,  and 
the  resisting  moment  will  be  less.  The  axis  of  moments 
will  be  taken  along  one  edge  of  the  bottom  of  the  footing. 
Case  III  will  deal  with  the  overturning  tendency  of  the  forces 
parallel  to  the  axis  of  the  bridge. 

54.  Overturning  Moments  of  Wind  Pressure: 
Case  I. — The  wind  pressure  on  the  train  is  equal  to  300 
pounds  per  linear  foot,  applied  7  feet  above  the  top  of  the 
rail  (Art.  46).  The  pressure  on  one-half  of  each  span  may 
be  assumed  to  be  transmitted  to  the  pier;  this  makes  the 
total  wind  pressure  on  the  train  300  X  (75  +  3  +  75)  =  45,900 
pounds,  acting  at  a  distance  (see  Fig.  16,  side  elevation)  of 


i 


BRIDGE  PIERS  AND  ABUTMENTS 


O 

D 


1 


7  +  4+1  +  22  +  3  +  2  +  16  +  2  +  4  =  61  feet  above  the 
bottom  of  the  footing.  The  overturning  moment  of  this 
pressure  is,  then, 

45,900  X  61  =  2,799,900  foot-pounds 
The  wind  pressure  on  the  floor  is  30  X  4  —  120  pounds  per 
linear  foot,  applied  2  feet  below  the  top  of  the  rail.  Then, 
the  total  wind  pressure  on  the  floor  is 

120  X  (75  +  3  +  75)  =  18,360  pounds 
(The  distance  of  3  feet  between  the  centers  of  bearings  of 
the  trusses  is.  usually  counted  in  computing  wind  pressure, 
because  the  floor  and  truss  members  project  beyond  the 
theoretical  ends.)  The  distance  from  the  center  of  this 
pressure  to  the  bottom  of  the  pier  is  61  —  7  —  i  —  52  feet. 
Then,  the  overturning  moment  of  this  pressure  is 
18,360  X  52  —  954,700  foot-pounds 
The  wind  pressure  on  each  truss  is  30  X  8  =  240  pounds 
per  linear  foot,  and  where,  as  in  this  case,  there  is  a  train 
on  the  bridge,  it  is  assumed  that  there  is  no  shelter  for  the 
leeward  truss;  hence,  the  total  wind  pressure  on  the  trusses 
transmitted  to  the  pier  is  2  X  240  X  (75  +  3  +  75)  =  73,440 
pounds.  This  pressure  will  be  assumed  to  be  concentrated 
half  way  between  the  chords  of  the  trusses;  that  is,  38  feet 
above  the  bottom  of  the  pier.  Then,  the  overturning  moment 
of  this  pressure  is 

73,440  x  38  =  2,790,700  foot-pounds 
In  calculating  the  pressure  of  the  wind  on  the  pier,  and 
that  of  the  water  current,  it  is  inadvisable  to  waste  time  in 
any  unnecessary  refinement,  as  the  values  of  the  wind  and 
water  pressures  are  but  roughly  approximate.  The  width  of 
the  pier  subjected  to  the  pressure  of  the  wind  is  6  feet 
6  inches  at  the  bridge  seat,  6  feet  at  the  bottom  of  the 
bridge-seat  course,  and  6  feet  8  inches  at  high-water  level; 
then,  for  purposes  of  calculation,  a  uniform  width  of  6  feet 
6  inches,  or  6.5  feet,  may  be  used,  and  the  center  of  wind 
pressure  taken  3  feet  below  the  bridge  seat.  Then,  the 
exposed  area  is  6  X  6.5  =  39  square  feet,  and  the  wind 
pressure  is  30  X  39  =  1,170  pounds,  the  center  of  which  may 
be  taken  as  4  +  2  + 16  +  2  —  3  =  21  feet  above  the  bottom 


BRIDGE  PIERS  AND  ABUTMENTS 


S 


of  the  pier.  The  overturning  moment  of  this  pressure  is, 

then, 

1,170  X  21  =  24,600  foot-pounds 

55.  o  yertnrning  Moment  of  Pressure  Due  to 
Current:  Case  I. — The  intensity  of  pressure  due  to  the 
current  is  given  by  formula  1,  Art.  47.  In  the  present 
case,  since  the  velocity  of  the  water  at  the  surface  is  6  miles 
per  hour,  the  pressure  at  the  surface  is  2.96  X  62  —  106.56 
pounds  per  square  foot. 

The  intensity  decreases  uniformly  with  the  depth,  being 
1  Oft 

— ^ —  =  53.28  pounds  per  square  foot  at  the  bottom  of  the 

ice  and  drift,  half  way  between  the  surface  and  the  bottom. 
Then,  since  the  exposed  area  of  the  ice  and  drift  is  given  in 
the  data  as  6  X  18  =  108  square  feet,  the  total  pressure  is 

106.56  +  53.28N 


108  X 


=  8,631  pounds 


If  p  represents  the  intensity  of  pressure  at  the  surface,  A 
the  intensity  of  pressure  at  the  bottom  of  the  ice,  and  dx  the 
distance  from  the  surface  to  the  bottom  of  the  ice,  the  dis¬ 
tance  x0  from  the  surface  to  the  center  of  pressure  is  given 
by  the  formula 

_  (2 A  +  p)  dx 
°  3  (A  +  p) 

In  the  present  case,  p  =  106.56,  A  —  53.28,  and  dx  —  6  feet. 
Substituting  in  the  formula  gives 

2  X  53.28  +  106.56 


X0  = 


X  6  =  2 i  feet 


3  (53.28  +  106.56) 

Then,  the  distance  from  the  center  of  pressure  to  the  bot¬ 
tom  of  the  pier  is  4  -f  2  +  12  —  2f  —  15i  feet,  and  the  over¬ 
turning  moment  of  the  pressure  on  the  ice  and  drift  is 
8,631  X  15i  =  132,300  foot-pounds 
The  pressure  of  the  water  on  the  pier  below  the  ice  and 
drift  remains  to  be  considered.  It  has  already  been  found 
that  the  intensity  of  this  pressure  at  the  bottom  of  the  ice  is 
53.28  pounds  per  square  foot;  this  value  may  be  substituted 
for  A  in  formula  3,  Art.  47,  which  gives 

P  =  i  X  53.28  A 


36 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


The  exposed  area  is  6  feet  high  and  from  7  feet  8  inches 
to  8  feet  8  inches  in  width.  The  area  is,  then,  6  X  8i  =  49 
square  feet;  and,  therefore, 

P  =  i  X  53.28  X  49  =  1,305  pounds 
This  pressure  may  be  assumed  to  be  concentrated  at  one- 
third  the  distance  from  the  bottom  of  the  ice  to  the  bottom 
of  the  river;  that  is,  4  feet  above  the  latter,  or  10  feet  above 
the  bottom  of  the  footing.  Then,  the  overturning  moment 
due  to  this  part  of  the  pressure  is 

1,305  X  10  =  13,100  foot-pounds 

56.  Total  Overturning  Moment:  Case  I. — The  total 
overturning  moment  can  now  be  found  by  adding  the  six 
products  just  found.  It  is  as  follows: 


Foot-Pounds 

Wind  on  train .  2,799,900 

Wind  on  floor .  954,700 

Wind  on  trusses .  2,790,700 

Wind  on  pier .  24,600 

Water  on  ice  and  drift  .  .  . .  132,300 

Water  on  pier  below .  13,100 


Total  overturning  moment  .  .  .  .  .  6,715,300 

If  the  track  were  on  a  curve,  the  centrifugal  force  of  the 
train  would  be  computed,  and  its  moment  about  the  base  of 
the  footing  added  to  the  moment  already  found. 

57.  Resistance  to  Overturning:  Case  I. — The  resist¬ 
ance  to  overturning  is  provided  by  the  weight  of  the  train, 
bridge,  and  pier.  The  resisting  moment  of  each  is  found  by 
multiplying  the  weight  by  the  distance  of  a  vertical  line 
through  its  center  of  gravity  from  the  down-stream  lower 
edge  of  the  footing. 

58.  Resisting  Moment  Due  to  Weight  of  Bridge 
and  Cars:  Case  I. — It  will  be  assumed  that,  when  both 
spans  supported  by  the  pier  are  fully  loaded,  one-half  the 
load  on  each  span,  together  with  3  feet  between  the  spans, 
is  supported  by  the  pier,  which  makes  the  total  weight 
of  unloaded  or  empty  cars  800  X  (75  +  3  +  75)  =  122,400 


BRIDGE  PIERS  AND  ABUTMENTS 


pounds.  The  horizontal  distance  from  the  center  of  the 
track  to  the  lower  edge  of  the  footing  is  seen  in  Fig.  16  to 
be  17  feet;  then,  the  resisting  moment  of  the  empty  train  is 

122,400  X  17  =  2,080,800  foot-pounds 
In  a  similar  manner,  the  resisting  moment  of  the  bridge  is 
found  to  be 

2,500  X  (75  +  3  +  75)  X  17  =  382,500  X  17 
=  6,502,500  foot-pounds 


59.  Resisting  Moment  Due  to  Weiglit  of  Pier: 
Case  I. — The  weight  of  the  pier  must  be  computed  in  two 
parts.  The  part  above  the  water  level  is  taken  at  its  actual 
weight.  The  part  immersed  in  water  is  decreased  in  weight 
on  account  of  the  buoyant  effort  of  the  water;  deduction  is 
made  by  decreasing  the  weight  per  cubic  foot  of  the  masonry 
by  62.5  pounds,  the  weight  of  a  cubic  foot  of  water. 

The  accurate  calculation  of  the  location  of  the  center  of 
gravity  for  each  part  of  the  pier  is  very  tedious,  and  it  is 
sufficiently  accurate 
in  practice  to  make 
use  of  an  approxi¬ 
mate  method  that  re¬ 
quires  less  work  and 
gives  close  enough 
results.  In  the  present  case,  the  pier  may  be  assumed  to  be 
composed  of  horizontal  layers  2  feet  thick,  each  layer  having 
a  uniform  horizontal  cross-section  equal  to  that  at  the  center 
of  its  height,  and  the  center  of  gravity  being  taken  at  the 
center  of  symmetry.  The  horizontal  cross-section  of  each 
layer  with  pointed  ends  will  then  have  the  appearance  shown 
in  Fig.  17,  the  area  A  being  given  by  the  formula: 

a  +  a!s 


A  =lc  + 


X  b 


The  values  of  c ,  a ,  and  b  for  the  different  layers  can  be 

calculated  from  the  dimensions  of  the  pier  given  in  Fig.  16. 

Commencing  with  the  bridge-seat  course,  and  continuing 
downwards,  the  volumes  of  the  layers  2  feet  thick  are  as 
follows: 


BRIDGE  PIERS  AND  ABUTMENTS 


*>Q 

/>o 


§82 


Bridge-seat  course, 

2  X  (20'  3"  +  3~)  x  6'  6"1 

First  2-foot  layer, 

2  X 


20'  4"  +  3'  1"  +  3'_1"  )  x  e'  2" 


] 


Second  2-foot  layer, 

3'  3"  +  3'  3'" 


2  X 


2P  + 


X  6'  6" 


] 


=  305.5  cu.  ft. 


288.81  cu.  ft. 


=  315.25  cu.  ft. 


Third  2-foot  layer, 
2  X 


(21'  8"  +  3'  5"  +  3'  5"^  x  6'  10"!  =  342.81  cu.  ft. 


Fourth  2-foot  layer, 

3/  7//  +  3/  7//> 


2  X 


22'  4 "  + 


X  T  2" 


] 


Fifth  2-foot  layer, 

3'  9"  +  3'  9//N 


2  X 


23'  + 


X  T  6" 


] 


=  371.47  cu.  ft. 


=  401.25  cu.  ft. 


Sixth  2-foot  layer, 

23'  8"  +  -  H"  +  3'  n"j  x  T  10" j  =  432.14  cu.  ft. 


2  X 

Seventh  2-foot  layer, 
2  X 

Eighth  2-foot  layer, 

2  X 


(24'  4"  +  £-!".+  4'  1"^  x 2„ j 


=  404.14  cu.  ft. 


25'  +  4'  ?J"  +  —  3 -'j  x  8'  6"J  =  497.25  cu.  ft. 


Ninth  2-foot  layer, 

2'  5"  +  2'  5"N 


2  X 


30'  8"  + 


X  9'  10" 


] 


650.64  cu.  ft. 


The  base,  4  feet  deep,  may  be  considered  as  one  layer: 

4  X  37  X  11  -  1,628  cubic  feet 
The  resisting  moment  of  the  portion  above  the  water 
will  now  be  found  by  multiplying  the  volume  of  each  of  the 
layers  by  the  assumed  weight  of  the  masonry,  150  pounds  per 
cubic  foot,  and  then  multiplying  each  of  these  products  by 
the  lever  arm  of  the  respective  layer.  The  resisting  moment 


§  82  BRIDGE  PIERS  AND  ABUTMENTS 


39  * 


of  the  portion  in  the  water  will  be  found  by  multiplying:  the 
volume  of  each  layer  by  150  —  62.5,  or  87.5,  pounds  per 
cubic  foot,  and  then  multiplying:  each  product  by  the  lever 
arm  of  that  layer.  The  resisting*  moments  are  as  follows: 

Bridge-seat  course,  Foot-Pounds 


(305.5  X  150)  X  17' 
First  2-foot  layer, 

(288.81  X  150)  X  17' 1"  = 
Second  2-foot  layer, 
(315.25  X  150)  X  17' 3"  = 
Third  2-foot  layer, 

(342.81  X  150)  X  17'  5"  = 
Fourth  2-foot  layer, 
(371.47  X  87.5)  X  17'  7"  = 
Fifth  2-foot  layer, 

(401.25  X  87.5)  X  17'  9"  = 
Sixth  2-foot  layer, 

(432.14  X  87.5)  X  17'  11"  = 
Seventh  2-foot  layer, 
(464.14  X  87.5)  X  18'  1"  = 
Eighth  2-foot  layer, 
(497.25  X  87.5)  X  18'  3"  = 
Ninth  2-foot  layer, 

(650.64  X  150)  X  18'  6"  = 
Base  layer, 

(1,628  X  150)  X  18' 6"  = 


=  45,825  X  17'  - 

779,025 

43,322  X  17' 1"  = 

740,084 

47,288  x  17' 3"  = 

815,718 

51,422  x  17' 5"  = 

895,600 

32,504  X  17'  7"  = 

571,530 

35,109  X  17' 9"  = 

623,185 

37,812  X  17' 11"  = 

677,465 

40,612  X  18'  1"  = 

734,400 

43,509  X  18' 3"  = 

794,039 

97,596  X  18' 6"  = 

1,805,526 

244,200  X  18' 6"  = 
Total, 

4,517,700 

12,954,300 

The  total  moment  is  given  to  six  significant  figures,  as  a 
closer  value  would  be  an  unnecessary  refinement. 


60.  Total  Resisting  Moment:  Case  I. — The  total 
resisting  moment  is  equal  to  the  sum  of  those  just  found, 


and  is  as  follows: 

Foot-Pounds 

Weight  of  empty  train  . .  2,080,800 

Weight  of  bridge  .  6,502,500 

Weight  of  pier . 12,954,300 

Total  resisting  moment .  21,537,600 

135—30 


40 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


61.  Factor  of  Safety  Against  Overturning:  Case  I. 
Dividing-  the  total  resisting  moment  found  in  the  preceding 
article  by  the  total  overturning  moment  found  in  Art.  56 
gives  for  the  factor  of  safety  against  overturning 

21,537,600  =  3  2 
6,715,300 

62.  Overturning  Moments:  Case  II. — In  the  second 
case,  it  is  assumed  that  there  is  no  train  on  the  bridge,  and 
so  there  is  no  overturning  moment  due  to  the  wind  pressure 
on  the  train.  The  wind  pressure  in  this  case  is  assumed  to 
be  50  pounds  per  square  foot  (Art.  46);  therefore,  the  over¬ 
turning  moments  due  to  this  pressure  on  the  bridge  and  on 
the  pier  can  be  found  by  multiplying  those  found  in  Art.  54 
by  U.  This  gives  the  moments  as  follows: 

Wind  on  floor, 

954,700  X  to  =  1,591,200  foot-pounds 
Wind  on  trusses, 

2,790,700  X  to  =  4,651,200  foot-pounds 
Wind  on  pier, 

24,600  X  to  =  41,000  foot-pounds 

The  overturning  moments  due  to  the  current  are  the  same 
as  found  in  Art.  55.  Then,  the  total  overturning  moment  is 
1,591,200  +  4,651,200  +  41,000  +  132,300  +  13,100 
=  6,428,800  foot-pounds 

63.  Resisting  Moments:  Case  II. — The  resisting 
moments  in  this  case  are  the  same  as  before,  with  the  excep¬ 
tion  of  that  due  to  the  weight  of  the  train,  which  is  here 
omitted.  The  total  resisting  moment  is,  then: 

Foot-Pounds 


Weight  of  bridge .  6,502,500 

Weight  of  pier .  12,954,300 

Total  resisting  moment .  19,456,800 


64.  Factor  of  Safety  Against  Overturning:  Case  II. 
The  factor  of  safety  against  overturning,  in  this  case,  is 

19.456.800  _  o 

6.428.800 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


41 


65.  Overturning  Parallel  to  Axis  of  Bridge: 
Case  III. — The  principal  force  tending-  to  overturn  the  pier 
in  the  direction  of  the  bridge  is  the  longitudinal  thrust  of  the 
train.  Under  some  conditions,  wind  may  blow  approximately 
in  the  direction  of  the  bridge,  but  the  effect  of  this  force  is 
so  small  compared  with  the  longitudinal  thrust  that  it  can  be 
neglected  with  safety.  In  order  to  get  the  greatest  force, 
the  maximum  weight  of  the  train  (4,000  pounds  per  linear 
foot,  Art.  52)  must  be  used.  Since  the  pier  supports  two 
fixed  ends  (Art.  52),  the  weight  of  306  feet  of  train,  or 
1,224,000  pounds,  may  be  assumed  to  affect  one  pier. 
Then  (Art.  51),  the  longitudinal  thrust  is  .20  X  1,224,000 
--  244,800  pounds,  acting  horizontally  at  the  bridge  seat,  or 
24  feet  above  the  bottom  of  the  footing.  Half  of  this  is 
usually  assumed  to  be  resisted  by  the  rails.  The  other  half 
causes  an  overturning  moment  about  the  lower  side  edge 
of  the  footing,  whose  value  is 

122,400  X  24  =  2,937,600  foot-pounds 

66.  Resisting  Moment:  Case  III. — The  resisting 
moment  is  provided  by  the  weight  of  the  bridge  and  trains 
for  a  distance  of  75  +  3  -f-  75  feet,  and  by  the  weight  of  the 
pier.  The  resisting  moment  offered  by  the  bridge  and 
train  is 

(2,500  -f  4,000)  X  153  X  5.5  =  5,469,750  foot-pounds 

The  weight  of  the  pier,  making  allowance  for  the  buoyant 
effort  of  the  water,  can  be  found  from  Art.  59  to  be  719,200 
pounds.  The  resisting  moment  due  to  this  weight  is 
719,200  X  5.5  =  3,955,600  foot-pounds.  The  total  resisting 
moment  is 

5,469,750  +  3,955,600  =  9,425,400  foot-pounds 

67.  Factor  of  Safety  Against  Overturning:  Case  III. 
Dividing  the  resisting  moment  by  the  overturning  moment 
gives  the  factor  of  safety  against  overturning: 

9,425,400  =  3  9 
2,937,600 

68.  Sliding. — The  horizontal  forces,  such  as  wind  pres¬ 
sure  and  longitudinal  thrust,  tend  to  make  the  upper  part  of 


42 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


the  pier  slide  on  the  lower  part.  The  resistance  to  sliding 
is  equal  to  the  vertical  load  multiplied  by  the  coefficient  of 
friction.  The  coefficient  of  friction  for  granite  may  be  taken 
as  .65.  Three  cases  must  be  considered,  in  the  same  way  as 
in  the  case  of  overturning. 

69.  Factor  of  Safety  Against  Sliding:  Case  I. — The 
horizontal  forces  in  this  case  have  been  found  in  the  prece¬ 
ding  pages.  They  are:  wind  on  train,  45,900  pounds;  wind 
on  floor,  18,360  pounds;  wind  on  trusses,  73,440  pounds; 
wind  on  pier,  1,170  pounds;  water  on  ice  and  drift,  8,631 
pounds;  water  on  pier,  1,305  pounds;  total,  148,800  pounds. 

The  vertical  loads  are  as  follows:  weight  of  empty  train, 
122,400  pounds;  weight  of  bridge,  382,500  pounds;  weight  of 
pier,  719,200  pounds;  total,  1,224,100  pounds.  Then,  the 
resistance  to  sliding  is  1,224,100  X  .65  =  795,665  pounds, 
and  the  factor  of  safety  against  sliding  is 

795,665  _  r  o 
148,800  "  ’ 

70.  Factor  of  Safety  Against  Sliding:  Case  II. — The 
horizontal  forces  in  this  case  can  be  found  in  the  same 
way  as  in  the  preceding  pages.  They  are:  wind  on  floor, 
M  X  18,360  =  30,600  pounds;  wind  on  trusses,  f  o'  X  73,440 
=  122,400  pounds;  wind  on  pier,  X  1,170  =  1,950  pounds; 
water  pressure,  9,936  pounds;  total,  164,900  pounds. 

The  vertical  loads  are  as  follows:  weight  of  bridge, 
382,500  pounds;  weight  of  pier,  719,200  pounds;  total, 
1,101,700  pounds.  Then,  the  resistance  to  sliding  is 
1,101,700  X  .65  =  716,100  pounds,  and  the  factor  of  safety 
against  sliding  is 

716,100  =  .  3 
164,900 

71.  Factor  of  Safety  Against  Sliding:  Case  III. 
The  only  horizontal  force  that  need  be  considered  in  the 
present  case  is  the  longitudinal  thrust  of  122,400  pounds 
(Art.  65).  The  vertical  forces  are  as  follows:  weight  of 
train  and  bridge,  6,500  X  153  =  994,500  pounds;  weight  of 
pier,  719,200  pounds;  total,  1,713,700  pounds.  Then,  the 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


43 


resistance  to  sliding  is  1,713,700  X  .65  =  1,113,900  pounds, 
and  the  factor  of  safety  against  sliding  is 

1,113,900  =  9  1 
122,400 

72.  Sliding  on  Foundation. — In  the  three  preceding 
articles,  the  entire  weight  of  pier  was  used,  so  that  the 
factor  of  safety  relates  to  a  surface  at  or  near  the  bottom  of 
the  pier.  The  tendency  to  slide  is  greater  at  the  bottom 
than  at  any  other  height,  and  it  has  been  assumed  that  the 
pier  rested  on  rock.  Piers  of  the  size  under  consideration 
usually  extend  down  to  rock  or  very  hard  strata,  and  so  the 
method  outlined  will  give  the  proper  factor  of  safety  if  the 
foundations  are  first  class. 


73.  Pressure  on  Subfoundation. — When  the  load  on  a 
pier  is  vertical  and  the  center  of  gravity  of  the  base  is  ver¬ 
tically  under  the  center  of  the  load,  the  pressure  on  the 
subfoundation  is  evenly  distributed,  and  the  intensity  is  found 
by  dividing  the  load  by  the  area  of  the  base.  When  the 
center  of  gravity  of  the  base  is  not  directly  under  the  center 
of  the  load,  or  when  horizontal  forces  act  on  a  pier,  the 
pressure  is  unevenly  distributed  over  the  base.  The  effect 
of  horizontal  forces  is  shown  in  Figs.  18  and  19.  When  the 
only  load  on  a  pier  is  a  vertical  load,  the  line  of  action  of  the 
pressure  on  the  subfoundation  may  be  represented  by  the  ver¬ 
tical  line  l  m.  When  a  horizontal  force  also  acts  on  the  pier, 
it  is  represented  by  the  line  In;  the  line  l o,  the  resultant 
of  / rh  and  In ,  represents  the  line  of  action  of  the  pressure  on 
the  base.  Fig.  18  shows  the  condition  when  the  horizontal 
force  is  at  right  angles  to  the  pier,  and  Fig.  19  shows  the 
condition  when  the  horizontal  force  is  parallel  with  the  pier. 

Under  these  conditions,  the  line  of  pressure  does  not  pass 
through  the  center  of  the  base,  and  the  intensity  of  pressure 
varies.  The  formulas  for  finding  the  maximum  and  minimum 
intensities  of  pressure  are: 


W  6  Wd  6M  =  W  6(Wd  +  M) 
A  +  AL  +  AL  A  +  A  L 
W  _  6  Wd  _  6M  =  W_  6(Wd  +  M) 
A  AL  AL  A  AL 


(1) 

(2) 


44 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


in  which  px  =  maximum  intensity  of  pressure; 

p 3  =  minimum  intensity  of  pressure; 

W  —  total  vertical  load; 

A  =  area  of  base  of  pier; 

d  =  eccentricity,  or  distance  from  center  of  grav¬ 
ity  of  vertical  load  to  center  of  base; 

L  =  length  of  base  in  direction  of  horizontal  force; 
M  —  moment  of  horizontal  forces  about  base. 

In  order  to  find  the  maximum  intensity  of  pressure  on  the 
foundation,  two  cases  must  be  considered:  Case  I,  when 


there  is  a  full  load  on  the  bridge  and  the  horizontal  forces 
are  greatest  and  acting  in  the  direction  of  the  pier;  Case  II, 
when  there  is  a  full  load  on  the  bridge  and  the  horizontal 
forces  acting  at  right  angles  to  the  pier  are  greatest. 


BRIDGE  PIERS  AND  ABUTMENTS 


45 


S 


74.  Formula  1  of  the  preceding  article  is  used  to  find 
the  maximum  intensity  of  pressure,  in  order  to  see  if  it 
exceeds  the  allowable.  Formula  2  is  of  interest  only  when 
the  maximum  intensity  of  pressure  is  greater  than  twice  the 
average  pressure;  in  this  case,  there  is  a  tendency  for  one 
end  of  the  pier  to  rise,  and  under  this  condition  water  may 
get  under  it  and  disturb  the  subfoundation. 

In  calculating  the  value  W d  it  is  not  necessary  to  get  the 
location  of  the  center  of  gravity  of  the  vertical  loads.  It  is 
invariably  easier  to  multiply  each  vertical  load  by  the  distance 
from  its  line  of  action  to  the  center  of  the  base;  the  algebraic 
sum  of  all  these  products  is  equal  to  W d. 

75.  Maximum  Intensity  of  Pressure:  Case  I. 
The  value  of  L  is  given  in  Fig.  16  as  37  feet,  and,  since  the 
width  is  11  feet,  the  value  of  A  is  37  X  11  =  407  square  feet. 
The  value  of  W  is  found  by  adding  the  weight  of  the  train, 
that  of  the  bridge,  and  that  of  the  pier,  the  last  being 
decreased  to  allow  for  the  buoyant  effort  of  the  water. 
Since  the  maximum  weight  of  the  train  is  4,000  pounds 
and  that  of  the  bridge  is  2,500  pounds  per  linear  foot 
(Art.  52),  their  combined  weight  is 

(4,000  +  2,500)  X  (75  +  3  +  75)  =  994,500  pounds 

The  weight  of  the  pier,  decreased  by  the  buoyant  effort 
of  the  water,  is  found  from  Art.  69  to  be  719,200  pounds. 
The  value  of  W  is,  then,  994,500  +  719,200  =  1,713,700 
pounds. 

76.  Since  the  vertical  loads  do  not  act  through  the  center 
of  the  base,  it  is  also  necessary  to  find  the  value  of  W d. 
The  total  weight  of  bridge  and  train  that  comes  on  the  pier 
was  found  above  to  be  994,500  pounds.  This  acts  17  feet 
from  the  down-stream  end  of  the  pier  (see  Fig.  16);  that  is, 
1.5  feet  from  the  center,  making  the  value  of  Wd  for  this 
load  equal  to 

994,500  X  1.5  =  1,491,800  foot-pounds 

The  value  of  Wd  due  to  the  weight  of  the  pier  can  most 
easily  be  found  by  calculating  the  position  of  the  center  of 
gravity  of  the  pier.  Since  the  moment  of  the  weight  of  the 


46 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


pier  about  the  down-stream  end  (Art.  59)  is  12,954,300  foot¬ 
pounds,  and  the  weight  of  the  pier  (Art.  66)  is  719,200 
pounds,  the  distance  of  the  center  of  gravity  from  the  down¬ 
stream  end  is 


12,954,300  =  18  012i  feet 
719,200 

This  gives  18.5  —  18.0121  =  .4879  foot  for  the  distance 
from  the  center  of  gravity  of  the  pier  to  the  center  of  the 
foundation,  and  the  value  of  Wd  for  this  load  is 
719,200  X  .4879  =  350,900  foot-pounds 
The  total  value  of  Wd  is,  therefore, 

1,491,800  +  350,900  =  1,842,700  foot-pounds 
The  moment  of  all  the  horizontal  forces  about  the  base 
is  the  same  as  the  overturning  moment  found  in  Art.  56; 
namely,  6,715,300  foot-pounds.  Substituting  the  proper 
values  in  formula  1,  Art.  73,  we  have 

=  1,713,700  1,842,700  X  6  6,715,300  X  6 

px  407  +  407  X  37  +  407  X  37 

=  7,620  pounds  per  square  foot 
Since  this  result  is  much  less  than  twice  the  average  value 

4,211  pounds  per  square  foot^,  it  is  not  necessary  to 
consider  the  minimum  intensity  of  stress 


77.  Maximum  Intensity  of  Pressure:  Case  II. — In 
this  case,  the  resultant  of  all  the  vertical  loads  passes  through 
the  center  of  the  base.  Then,  since  the  eccentricity  is  zero, 
the  third  term  in  formulas  1  and  2,  Art.  73,  becomes 
zero,  and  need  not  be  considered.  The  values  of  W  and  A 
are  the  same  as  in  Case  I;  but  since  the  horizontal  forces  in 
this  case  are  assumed  to  act  at  right  angles  to  the  length  of 
the  pier ,  A  =11  feet.  The  moment  of  the  horizontal  forces 
about  the  base  is  the  same  as  that  found  in  Art.  65,  or 
2,937,600  foot-pounds.  Substituting  the  proper  values  in 
formula  1,  Art.  73,  gives 

=  1,713,700  2,937,600  X  6 

Pl  407  +  407  X  11 

=  8,148  pounds  per  square  foot 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


47  . 


Since  this  is  less  than  twice  the  average  value,  it  is  not 
necessary  to  consider  the  minimum  intensity. 

78.  Horizontal  Forces  Acting  in  Both  Directions. 
The  maximum  intensities  found  in  Cases  I  and  II  are  those 
that  occur  when  the  horizontal  forces  act  in  but  one  direc¬ 
tion.  Since  it  is  possible  for  them  to  act  in  both  directions 
at  the  same  time,  this  case  must  also  be  considered.  Under 
this  condition,  however,  since  it  will  probably  be  of  such 
rare  occurrence,  the  intensity  of  pressure  is  allowed  to  exceed 
the  working  pressure  by  25  per  cent.  In  Case  I,  the  maxi¬ 
mum  intensity  of  pressure  extends  for  the  full  width  of  the 
pier  at  one  end;  in  Case  II,  the  maximum  intensity  of  pres¬ 
sure  extends  for  the  full  length  of  the  pier  at  one  side.  The 
maximum  intensity  then  occurs  at  the  corner  where  these 
two  edges  meet,  and  is  equal  to  the  sum  of  the  different 
terms  obtained  in  Arts.  76  and  77,  each  term  being  used 

but  once.  For  example,  although  the  term  —  occurs  in 

A 

each  case,  it  is  used  but  once  in  finding  the  sum.  Then,  the 
total  intensity  at  one  corner  is 

4,211  +  733  +  2,676  +  3,937  =  11,557  pounds  per  square  foot 

If  the  intensity  of  pressure  found  in  Cases  I  and  II  does 
not  exceed  the  safe  intensity,  and  if  that  just  found  does  not 
exceed  the  safe  intensity  by  more  than  25  per  cent.,  the 
design  is  assumed  to  be  safe.  Otherwise,  the  dimensions  of 
the  pier  are  increased  and  the  foregoing  computations 
repeated.  Although  the  maximum  intensity  found  by  com¬ 
bining  the  two  cases  is  greater  than  twice  the  average,  no 
further  attention  need  be  paid  to  it.  This  high  pressure 
will  simply  affect  a  very  small  corner  of  the  pier. 


48 


BRIDGE  BIERS  AND  ABUTMENTS 


82 


ABUTMENT  DESIGN 

79.  The  method  of  arriving-  at  the  dimensions  of  an 
abutment  are  much  the  same  as  those  used  for  piers.  In  the 
first  place,  the  dimensions  necessary  to  satisfy  practical 
conditions  are  found;  then,  calculations  are  made  to  ascertain 
whether  the  abutment  satisfies  the  theoretical  conditions. 


PRACTICAL  CONSIDERATIONS 


GENERAL  FEATURES 

80.  Classes  of  Abutments. — There  are  three  general 
classes,  or  forms,  of  abutments:  the  wing  abutment;  the 
T  abutment;  and  the  U  abutment.  The  wing  abutment  con¬ 
sists  of  a  mass  of  masonry  extending  the  full  width  of  the 
bank  it  restrains.  It  usually  decreases  in  height  from  the 
edges  of  the  bridge  to  the  foot  of  the  bank.  Several  forms 
of  wing  abutments  are  shown  in  the  following  pages.  In  the 
T  abutment  there  is  a  face  wall,  called  the  head,  on  which 
the  bridge  rests,  and  a  wall  running  back  under  the  track  or 
road  to  the  top  of  the  bank,  as  shown  in  Figs.  20  and  21. 
This  wall  is  called  the  stem,  or  tail.  The  head  usually 
extends  beyond  the  stem  at  both  sides. 

In  the  U  abutment,  there  is  a  head  similar  to  that  in  the 
T  abutment;  instead  of  one  stem,  there  are  two  walls  running 
back  as  far  as  the  top  of  the  slope,  as  shown  in  Fig.  22.  These 
walls  are  even  with  the  outer  edges  of  the  roadway.  The 
space  between  the  walls  may  be  filled  with  earth  or  loose 
rock. 

81.  Bridge  Seat. — As  in  the  case  of  piers,  the  first  thing 
to  be  considered  is  the  size  of  the  top  of  the  abutment.  An 
abutment  usually  supports  one  end  only  of  a  span,  so  the 
width  of  the  bridge  seat  for  this  purpose  need  only  be  about 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


49 


/Base  of  Ba// 


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i_ j 

/  .. 

\ 

/Base  ofBa/7 


Fig.  21 


50 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


one-half  as  wide  as  that  of  a  pier.  On  account  of  the  parapet, 
the  bridge-seat  course  is  usually  continued  back  under  it.  The 
required  width  of  bridge  seat  and  the  width  of  the  parapet  at 
the  elevation  of  the  bridge  seat  control  the  width  of  the  top 
of  the  abutment.  The  ends  of  the  bridge  seat  are  carried  a 
few  feet  beyond  the  trusses,  or  girders,  or  to  the  edge  of  the 
roadway. 

82.  Parapet. — The  parapet,  or  back  wall,  of  an  abut¬ 
ment  is  simply  a  retaining  wall  to  prevent  the  earth  above  the 
bridge  seat  from  falling  down.  In  order  to  keep  it  from 


,Base  o/  Ra/Y 


tipping  over  or  sliding  forwards  on  account  of  the  pressure 
of  the  earth  and  of  the  traffic,  the  parapet  should  have  a 
width  at  the  bottom  of  from  .4  to  .5  the  height. 

For  a  distance  of  about  3  feet  down  from  the  top,  the  back 
of  the  parapet  should  be  given  a  smooth  batter,  usually  called 
the  frost  batter,  so  that  the  action  of  the  frost  cannot  move 
it.  The  face  of  the  parapet  should  be  set  back  far  enough 
from  the  end  of  the  bridge  so  that  that  end  will  not  hit  the 
parapet  when  the  bridge  expands.  A  distance  of  3  inches  is 


§  82  BRIDGE  PIERS  AND  ABUTMENTS  51  ' 

I 

usually  specified  as  the  closest  the  bridge  must  ever  come  to 
the  parapet. 

83.  Pedestal  Blocks. — The  remarks  given  in  Art.  23 
with  regard  to  pedestal  blocks  for  piers  apply  to  those 
required  for  abutments.  When  used  on  abutments,  it  is 
advisable  to  have  one  surface  of  the  block  in  contact  with 
the  parapet. 

84.  Pockets  in  Bridge  Seats. — Great  care  should  be 
taken  in  the  arrangement  of  blocks  and  parapets  on  bridge 
seats  that  no  pockets  are  formed.  The  word  “pocket”  is 
usually  applied  to  portions  of  the  work  where  dirt  may 
collect  and  from  which  it  is  difficult  to  remove  it.  Since  the 
earth  behind  an  abutment  usually  extends  up  to  nearly  the 
top,  winds  usually  blow  some  of  it  over  the  parapet  on 
the  bridge  seat.  If  the  steelwork  is  near  the  pocket,  the  dirt 
will  pile  up  against  it,  absorb  moisture  from  the  air,  and  cause 
the  steel  to  corrode  rapidly.  Pockets  can  be  avoided  by  the 
use  of  end  floorbeams,  which  do  away  with  the  pedestal 
blocks,  and  by  continuing  the  parapet  straight  from  end  to 
end  of  the  abutment  so  the  wind  can  have  a  clean  sweep 
across.  For  this  purpose  it  is  advisable  to  have  the  main 
trusses  or  girders  at  least  1  foot  above  the  bridge  seat. 

85.  Batter. — The  front  faces  of  many  abutments  are 
made  plumb,  because  the  appearance  is  not  marred  here  as 
in  the  case  of  a  pier  with  both  faces  plumb.  It  is  somewhat 
better,  however,  to  give  the  face  a  batter  of  about  2  inch 
per  foot.  It  should  be  borne  in  mind  that  the  batter  of  the 
front  face  increases  the  length  of  the  span,  and,  therefore, 
that  batter  should  not  be  made  unnecessarily  large.  No 
standard  batter  is  used  at  the  back,  the  slope  being  con¬ 
trolled  by  the  top  width  and  the  required  width  of  base. 

86.  Width,  of  Base. — The  width  of  base  should  be 
determined  by  means  of  theoretical  considerations,  allowing 
for  the  pressure  at  the  back  due  to  the  earth  filling  increased 
by  the  weight  and  jar  of  the  traffic.  Generally,  it  is  not 
usual  in  practice  to  make  a  theoretical  determination  of  the 


52 


BRIDGE  PIERS  AND  ABUTMENTS 


82 

required  width  of  base,  but  to  make  the  width  a  certain 
fraction  of  the  height;  in  the  case  of  high  or  unusual  abut¬ 
ments,  however,  calculations  should  be  made.  It  has  been 
found  by  practical  experience  that  the  width  of  base  should 
be  from  three-eighths  to  one-half  the  distance  from  the  top  of 
the  fill  to  the  level  of  the  base.  For  first-class  stone  masonry 
or  solid  concrete,  three-eighths  of  the  height  is  sufficient;  for 
second-class  masonry,  one-half  the  height  should  be  used. 

87.  Footing;. — The  footing  course  of  an  abutment  does 
not  have  to  extend  beyond  the  back  of  the  masonry,  but  it 
should  extend  beyond  the  front  face.  This  is  due  to  the 
fact  that  the  overturning  tendency  causes  higher  pressure 
at  the  face  of  the  abutment,  and  the  footing  must  be 
extended  here  in  order  to  distribute  the  pressure  over  a 
greater  area.  In  some  cases,  several  footing  courses,  each 
projecting  beyond  the  one  above,  are  used. 


T  ABUTMENTS 

88.  Since  the  head  of  a  T  abutment  has  no  bank  to 
restrain,  it  may  be  made  just  wide  enough  at  the  top  to 
accommodate  the  bearing  plates  of  the  bridge,  and  the  front 
and  back  faces  may  be  continued  down  to  the  base  with 
a  slight  batter.  The  base  of  the  head  is  at  the  foot  of  the 
slope,  and  the  bank  slopes  up  to  the  end  of  the  stem. 
T  abutments  were  formerly  the  most  common,  because  of 
their  simplicity  and  of  the  fact  that  low-grade  masonry  could 
be  used.  On  the  other  hand,  the  T  abutment  requires  much 
more  masonry,  on  account  of  the  stem,  than  abutments  of 
other  forms.  For  double-track  railroads  or  wide  streets,  the 
amount  of  masonry  is  excessive. 

The  most  serious  objection  to  this  form  of  abutment,  when 
used  for  railroad  bridges,  is  that  it  gives  a  support  to  the 
bridge  that  is  too  rigid,  making  riding  uncomfortable  to 
passengers  and  injurious  to  the  rolling  stock  and  track.  In 
some  cases,  1  or  2  feet  of  ballast  is  inserted  between  the 
track  and  the  masonry,  but  this  does  not  wholly  remove 
the  bad  effects  of  rigidity. 


§82 


BRIDGE  PIERS  AND  ABUTMENTS 


53 


U  ABUTMENTS 

89.  The  U  abutment  is  practically  a  wing-  abutment  in 
which  the  wings  are  parallel  to  the  track,  although  it  has 
more  the  appearance  of  a  T  abutment.  The  slope  of  the 
bank  is  sometimes  carried  down  outside  the  wings,  but  more 
frequently  the  space  between  the  wings  is  filled  with  earth  or 
broken  stone.  In  the  latter  case,  the  two  wings  must  be 
designed  in  the  same  way  as  a  retaining  wall.  When  the 
earth  is  allowed  to  run  down  outside  the  wings,  they  may  be 
made  about  three-quarters  the  width  required  by  the  other 
condition;  this  is  permissible  because  the  earth  outside  the 
wings  helps  to  support  them. 


WING  ABUTMENTS 


90.  Types  of  Wings. — There  are  three  common  types 
of  wing  abutments;  namely,  the  straight-wing  abutment, 


Fig.  23 


Fig.  23,  in  which  the  face  of  the  wings  is  in  the  same  plane 
as  the  face  of  the  abutment  proper;  the  flaring-wing 


54 


§82  BRIDGE  PIERS  AND  ABUTMENTS  55 


135—31 


56 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 

abutment,  Fig.  24,  in  which  the  faces  of  the  wings  make 
an  angle  with  the  face  of  the  abutment  proper;  and  the 
curved-wing  abutment,  Fig.  25,  in  which  the  wings  are 
curved.  In  general,  the  curved  surfaces  of  the  wings  start 
almost  normal  with  the  face  of  the  abutment  and  turn 
through  about  90°  until  they  are  at  right  angles  to  the  track. 

91.  Size  of  Wings. — Each  wing  starts  at  the  top  of  the 
abutment  and  decreases  in  height  until  it  reaches  the  foot  of 
the  bank,  where  the  height  reaches  zero.  The  top  surface 
of  the  wing  follows  approximately  the  intersection  of  the 
plane  of  the  wing  with  the  plane  of  the  slope  of  the  bank. 
In  Fig.  26,  (a)  represents  the  form  of  wing  that  might  be 
used  with  concrete,  while  (b)  and  (c)  indicate  the  forms  for 
stone  masonry.  The  inclined  line  in  (a)  is  smooth,  because 
it  is  easier  to  finish  concrete  in  this  manner.  The  forms  {b) 
and  (r)  are  stepped,  the  height  of  the  steps  being  the  same 


as  the  thickness  of  the  courses  of  the  stone.  In  order  to 
keep  the  earth  from  covering  the  wing,  the  steps  should  be 
carried  beyond  the  slope,  as  shown  in  {b).  To  save  masonry, 
the  steps  are  sometimes  made  shorter  and  the  earth  allowed 
to  cover  the  wing,  as  at  (c) . 

In  the  design  of  wings,  it  is  assumed  that  the  bank  has  a 
slope  of  li  horizontal  to  1  vertical.  When  the  earth  is 
allowed  to  run  over  on  the  steps,  as  at  (<:),  the  abutment 
presents  a  very  untidy  appearance,  and  the  extra  expense  of 
the  form  {b)  is  warranted  by  the  improved  appearance.  In 
the  form  shown  in  Fig.  26  (a),  the  top  of  the  wing  should  be 
from  6  to  12  inches  above  the  earth. 

92.  Toe  of  Wing. — When  it  is  necessary  to  keep  the 
earth  from  running  around  in  front  of  the  wing,  the  latter  is 


BRIDGE  PIERS  AND  ABUTMENTS 


57 


CO 

O-J 


continued  down  to  the  foot  of  the  slope.  When  flaring  wings 
are  used,  however,  it  is  allowable  for  the  earth  to  run  around 
somewhat,  unless  the  abutment  is  on  the  shore  of  the  stream. 
A  sketch  of  a  wing  in  which  this  was  done  is  shown  in  Fig.  24, 
the  broken  line  at  the  left  in  (a)  showing  the  foot  of  slope. 
Some  masonry  is -saved  by  adopting  this  method. 

The  thickness  of  a  wing  is  usually  the  same  at  the  top  as 
that  of  the  abutment  proper;  the  width  or  thickness  gradually 
decreases  until  the  toe  is  reached,  where  the  width  is  usually 
about  2  feet. 

93.  Straight-Wing  Abutments. — The  straight-wing 
form  of  abutment  is  particularly  fitted  for  bridges  over  city 
streets,  and  is  probably  the  most  economical  for  this  purpose. 
The  face  of  the  abutment  and  wings  is  placed  at  the  street 
line,  and  gives  a  good  appearance.  Since  in  this  case  it  is 
impossible  to  have  any  earth  in  front  of  the  abutment,  the 
wings  must  be  carried  to  the  ends  of  the  slopes. 

The  principal  advantage  in  the  use  of  straight-wing  abut¬ 
ments  for  railroad  bridges  is  that  in  case  an  increase  in  the 
number  of  tracks  is  made,  the  courses  can  be  so  arranged 
that  there  will  be  little  difficulty  in  extending  the  abutment. 
An  outline  of  a  straight-wing  abutment  is  shown  in  Fig.  23; 
(a)  is  a  plan  of  one  end  of  the  abutment,  (b)  is  an  elevation 
of  the  portion  shown  in  (a) ,  and  (c)  is  a  cross-section  through 
the  bridge  seat. 

In  some  cases,  this  form  of  abutment  is  slightly  modified 
by  making  the  back  straight,  and  thus  causing  the  wings  to 
make  a  slight  angle  with  the  face  of  the  abutment.  This  is 
not  desirable,  as  it  mars  the  appearance  somewhat,  and  also 
because  it  involves  extra  expense  in  stone  cutting  in  order 
to  form  the  angle. 

* 

94.  Flaring-Wing  Abutments.  —  For  abutments  at 
the  edge  of  a  river,  flaring  wings  are  usually  preferable  to 
other  wings.  They  give  a  greater  opening  for  the  stream 
above  the  bridge,  and  help  to  direct  the  current  into  the 
proper  channel,  thus  preventing  the  water  from  injuring  the 
foundation  by  getting  behind  the  abutment.  Where  the 


58 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


greatest  economy  is  desired,  the  wings  may  be  made  shorter 
and  the  earth  allowed  to  run  around  in  front,  as  previously 
shown  in  Fig.  24.  This  reduces  the  amount  of  masonry. 

If  the  masonry  is  first  class  and  well  bonded,  the  flaring- 
wing  abutment  gives  greater  stability,  for  overturning  or 
sliding  can  occur  only  when  one  part  of  the  abutment  tears 
away  from  the  other  part.  In  order  to  use  the  least  amount 
of  masonry  in  the  wings  when  the  earth  is  allowed  to  run 


around  in  front,  they  should  make  an  angle  of  about  30° 
with  the  plane  of  the  face  of  the  abutment  produced.  This 
is  the  angle  generally  used;  however,  for  greatest  efficiency 
at  a  stream  in  directing  the  flow  toward  the  opening,  the 
angle  should  be  about  10°,  and  the  wings  should  be  carried 
to  the  extreme  foot  of  the  bank,  in  order  to  keep  the  current 
from  washing  away  the  earth  and  thereby  undermining  the 
abutment. 

95.  Curved-Wing  Abutments. — The  principal  reason 
for  the  use  of  abutments  with  curved  wings  is  the  improved 


82 


BRIDGE  PIERS  AND  ABUTMENTS 


59 


appearance.  With  very  high  abutments,  where  filling  mate¬ 
rial  cannot  be  easily  obtained,  there  is  the  additional  advan¬ 
tage  that  they  save  filling.  Fig.  25  shows  one  end  of  an 
abutment  with  curved  wings.  The  front  elevation,  shown  at 
(b) ,  indicates  that  the  top  of  the  curved  wing  follows  the 
slope  of  the  bank. 

Another  form  of  curved  wing  is  shown  in  Fig.  27.  This 
form  has  the  advantage  that,  like  flaring  wings,'  it  easily 
deflects  the  current.  It  also  has  a  pleasing  appearance,  and 
is  not  so  expensive  as  some  other  forms  of  curved  wings. 


SKEW  ABUTMENTS 

96.  It  is  frequently  necessary  to  build  abutments  at  some 
other  angle  with  the  bridge  than  90°.  The  bridge  is  then  a 
skew  bridge,  and  the  abutments  are  called  skew  abut¬ 
ments.  For  such  construction,  straight  wings  may  be 
used,  as  shown  in  outline  by  AD  in  Fig.  28.  One  end  of 


each  abutment  can  be  made  shorter  than  the  other;  this  can 
be  seen  in  the  figure  at  A  and  D,  both  of  these  points  being 
at  the  proper  distance  from  the  top  of  the  slope  C.  In  many 
cases,  the  wing  is  made  to  extend  from  C  to  A  at  right 
angles  to  the  bridge.  This  really  makes  a  flaring  wing  for 
this  end  of  the  abutment,  as  shown  in  Fig.  29.  In  case  there 
is  no  water  at  the  face  of  the  abutment,  masonry  may  be 
saved  by  allowing  the  earth  to  run  around  the  end  of  the 
wing. 


/Nufura/  Surface  of  Ground 


§82 


BRIDGE  BIERS  AND  ABUTMENTS 


<>1 

In  the  design  of  skew  abutments,  great  care  should  be 
taken  that  the  bridge  seat  is  wide  enough.  As  the  bearing 
plates  are  set  on  a  skew,  they  take  up  more  width  on  the 
bridge  seat  than  when  there  is  no  skew. 


PIER  ABUTMENTS 

97.  When  a  trestle  is  built  across  a  valley,  the  greater 
part  of  the  distance  is  spanned  by  girders  or  trusses.  Near 
the  ends,  however,  it  is  usually  found  more  economical  to 
fill  for  a  short  distance.  It  is  then  necessary  to  build  an 


\ 

7' 

If — 1 

1 

1 

/ 

\ 

e 


abutment  in  this  new  ground  for  the  end  of  the  trestle. 
This  is  usually  accomplished  las  shown  in  Fig.  30.  A  pier  is 
built  on  the  natural  surface  of  the  ground,  and  the  fill 
allowed  to  run  around  in  front  of  it.  This  form  of  structure 
is  called  a  pier  abutment  (see  Art.  2). 


62 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


THEORETICAL  CONSIDERATIONS 

98.  Forces  to  be  Resisted. — On  account  of  the  fact 
that  an  abutment  is  in  contact  with  an  earth  fill,  it  can  over¬ 
turn  or  slide  in  but  one  direction;  namely,  away  from  the 
bank.  It  is  prevented  from  moving  sidewise  by  the  friction 
of  the  earth  behind  it  and  also  by  the  wings.  The  forces 
that  act  to  overturn  the  abutment  are  the  pressure  of  the 
earth  and  the  longitudinal  thrust  of  the  train. 

99.  Calculations. — The  pressure  of  the  earth  is  found 
in  the  manner  explained  in  Retaining  Walls ,  the  weight  of 
the  train  or  other  loads  being  added  to  the  weight  of  the 
earth  as  the  surcharge.  The  longitudinal  thrust  is  found 
in  the  manner  given  for  piers  in  Art.  51.  The  methods 
of  determining  the  factors  of  safety  against  overturning 
and  sliding,  and  the  intensity  of  pressure  on  the  subfounda¬ 
tion,  are  the  same  as  for  piers. 


CONSTRUCTION 


MATERIALS 

100.  The  materials  most  used  for  piers  and  abutments 
are  stone,  concrete,  and  timber.  In  addition  to  these,  large 
cylinders  having  steel  or  cast-iron  outside  surfaces  and  con¬ 
crete  interiors  are  sometimes  used. 

101.  Stone. — The  most  common  material  is  stone. 
The  very  best  stone  available  is  generally  selected.  There 
is  little  economy  in  using  poor  masonry,  as  more  is  required 
than  when  good  masonry  is  used.  Granite,  when  available, 
is  the  best  stone,  because  it  is  hard,  strong,  and  durable, 
and  can  be  brought  to  required  shapes  more  easily  than 
other  stones  of  equal  strength.  Its  only  weakness  is  that  it 
disintegrates  easily  when  exposed  to  fire;  but  this  danger 
seldom  occurs  in  piers  and  abutments. 


82 


BRIDGE  PIERS  AND  ABUTMENTS 


63 


Syenite,  gneiss,  quartz,  trap,  and  porphyry  are  also  excel¬ 
lent  stones,  but  are  hard  to  work,  and  so  are  seldom  used  for 
bridge  masonry.  Quartzite  also  is  a  good  stone.  When  these 
stones  are  not  available,  some  grades  of  sandstone  or  lime¬ 
stone  may  take  their  place. 

Certain  kinds  of  stone  are  not  suited  for  bridge  masonry, 
on  account  of  their  tendency  to  disintegrate  from  the  action 
of  frost,  acids,  attrition,  or  fire.  As  a  general  rule,  there  is 
less  danger  from  frost  in  those  stones  that  are  compact  and 
non-absorptive  than  in  porous  stones,  which  permit  water 
to  enter  and  freeze  inside.  A  compact  stone  is  also  less 
liable  to  absorb  acids  from  the  air  or  the  water  than  a 
porous  stone. 

Most  sandstones  are  very  absorptive,  and  the  cementing 
material  is  easily  dissolved  if  it  consists  of  lime,  iron  oxide, 
clay,  magnesia,  or  feldspar.  Quartzite,  or  sandstone  in  which 
the  cementipg  material  is  of  quartz,  is  less  permeable  and 
contains  less  matter  that  can  easily  dissolve.  A  stratified 
stone  is  also  more  liable  to  disintegration  than  an  unstratified 
stone,  because  it  offers  straight  paths  between  the  strata  for 
moisture  to  reach  the  interior,  and  also  because  it  offers  easy 
cleavage  lines.  In  case  stratified  stones  are  used,  they  should 
be  placed  so  that  the  strata  will  be  horizontal. 

Limestone  consists  chiefly  of  carbonate  of  lime,  and  is 
easily  injured  by  nitric  and  by  hydrochloric  acid.  A  mag¬ 
nesian  limestone  is  much  more  durable  than  a  pure  limestone. 
Exposure  to  fire  reduces  the  limestone  to  almost  pure  lime, 
which  is  soluble  in  water. 

i 

102.  Concrete. — Concrete,  both  plain  and  reinforced, 
is  much  used  for  bridge  masonry.  It  is  more  durable  than 
many  limestones  and  sandstones,  and,  when  properly  made 
and  laid,  is  sometimes  as  strong  and  durable  as  granite. 
The  principal  advantages  of  concrete  are  its  comparatively 
low  cost  and  the  fact  that  it  makes  a  monolithic  structure. 
A  Portland-cement  concrete  mixed  in  the  proportions  of  1:2:4 
with  hard,  angular,  well-graded  stones  for  the  aggregate,  is 
a  sufficiently  good  material  for  all  bridge  masonry.  In  many 


64 


BRIDGE  PIERS  AND  ABUTMENTS 


82 


cases  stone  is  used  for  the  face  of  an  abutment  or  pier,  and 
the  interior  is  made  of  concrete. 

103.  Timber. — In  temporary  construction,  and  in  some 
cases  where  time  does  not  permit  the  erection  of  masonry 
supports,  bridges  are  supported  by  timber  structures.  These 
usually  consist  of  several  framed  or  pile  bents  set  parallel, 
and  close  to  one  another.  The  abutments  in  this  case  are 
similar  to  the  end  bents  described  in  Trestles ,  except  that 
more  than  one  bent  may  be  used.  In  permanent  structures, 
wood  should  never  be  used  except  for  the  foundations,  and 
when  so  used  the  top  of  the  timber  construction  should  be 
below  the  lowest  level  the  water  ever  reaches. 

104.  Joints. — The  joints  in  stone  masonry  should  be 
made  as  thin  as  possible,  and  rich  Portland-cement  mortar 
used.  There  is  no  economy  in  using  a  first-class  stone  and 
then  binding  the  whole  together  with  a  poor  mortar. 

105.  Steel  Cylinders. — Sometimes,  piers  are  made  of 
steel  or  cast-iron  cylinders  filled  with  concrete.  These  are 
easy  to  place  and  are  well  adapted  to  soft  soils.  Short  sec¬ 
tions  are  placed  and  bolted  one  on  top  of  another,  and  the 
whole  is  forced  into  the  ground.  The  interior  is  usually 
excavated  while  the  cylinder  is  being  driven,  and  then  filled 
with  concrete.  In  this  form  of  construction,  a  pier  usually 
consists  of  two  cylinders  with  a  set  of  heavy  girders  extend¬ 
ing  across  their  tops. 


DETAILS 

106.  Specifications. — The  specifications  for  bridge 
masonry  may  be  substantially  the  same  as  for  retaining  walls, 
the  principal  difference  being  in  the  bridge  seat.  All  the 
masonry  above  the  footing  should  be  first-class  stone  laid  in 
Portland-cement  mortar.  The  stones  should  be  laid  with 
horizontal  and  vertical  joints,  the  courses  being  from  18  to 
24  inches  in  height.  The  faces  can  be  left  rough,  provided 
no  point  projects  more  than  3  inches  beyond  the  edge  of 
the  joint.  All  joints  should  be  perfectly  straight. 


§82  BRIDGE  PIERS  AND  ABUTMENTS  65 

The  bridge-seat  course  should  be  bush-hammered  on  top, 
and  brought  to  a  level  surface  at  the  proper  elevation  for 
the  bearing  plates.  All  joints  above  the  footing  should  be 
pointed  with  neat  cement  with  a  i-inch  semicircular  bead, 
except  at  the  top  of  the  bridge  seat,  where  they  should  be 
level  with  the  stone.  For  bonding  purposes,  not  less  than 
one-quarter  of  the  face  should  be  composed  of  headers.  All 
stones  should  be  at  least  4  feet  long,  but  no  stone  should  be 
longer  than  five  times  its  height.  On  account  of  the  impact 
of  ice  and  drift,  the  masonry  near  the  water-line  of  a  pier  in 
a  stream  may  be  of  a  better  class  than  the  remainder.  The 
footing  may  be  of  coarse  rubble,  with  stones  about  i  cubic 
yard  in  size. 

107.  Bridge-Seat  Course. — The  bridge-seat  course 
should  be  so  designed  that  the  stones  will  have  a  good  bond. 
Except  where  the  bearing  is  very  large,  there  should  be  but 
one  stone  under  the  bearing  plate.  In  general,  the  joints 
should  be  kept  as  far  as  possible  from  the  edges  of  the  bear¬ 
ing  plates.  The  top  of  each  stone  under  a  bearing  plate 
should  be  dressed  smooth.  Pedestal  blocks  should  not  be 
used  for  a  height  less  than  8  inches,  and  the  height  should 
not  be  less  than  one-fifth  the  length  of  the  block.  For  a 
small  difference  in  elevation  of  the  bearings,  castings  may 
be  used,  or  the  bridge-seat  stones  may  be  made  of  different 
thicknesses,  as  previously  explained  in  connection  with 
Fig.  5  (b). 

108.  Parapets. — The  parapet  of  an  abutment  helps  to 
bond  the  bridge-seat  stones.  The  latter  should  extend  at 
least  9  inches  behind  the  face  of  the  parapet.  When  prac¬ 
ticable,  it  is  advisable  to  have  the  bridge-seat  stones  extend 
entirely  across  the  top  of  the  abutment.  There  is  no  neces¬ 
sity  for  dressing  the  face  of  a  parapet.  In  railroad  bridges, 
it  is  customary  to  have  the  top  of  the  parapet  from  8  to  12 
inches  below  the  base  of  rail,  and  to  rest  a  tie  on  its  top. 
In  highway  bridges,  it  was  customary  to  have  the  top  of  the 
parapet  even  with  the  street  surface.  This  gave  rise  to  an 
uncomfortable  jar  in  passing  over  the  masonry.  At  present, 


66 


BRIDGE  PIERS  AND  ABUTMENTS 


§82 


the  top  of  the  parapet  is  finished  off  below  the  street  sur¬ 
face,  and  the  flooring  is  continued  across. 

109.  Pedestals  and  Piers  for  Trestles. — The  small 
depth  of  a  trestle  pier  requires  great  care  in  properly  bonding 
the  separate  stones,  so  that  the  loads  shall  be  properly  dis¬ 
tributed  over  the  base.  Fig.  7  shows  an  outline  of  a  pier 
suitable  for  the  support  of  a  high  trestle  bent.  When  sepa¬ 
rate  pedestals  are  used,  the  top  of  each  should  be  a  single 
stone.  Even  when  concrete  is  used,  the  cap  should  be  of  a 
good  hard  stone.  Fig.  31  shows  a  stepped  pedestal  of  stone 

masonry.  When  the  lower 
part  is  concrete,  the  sides 
are  sloped,  as  shown  in 
dotted  lines. 

110.  Batter.  —  The 
batter  of  the  face  of  a  pier 
or  of  an  abutment  is 
obtained  by  cutting  the 
face  of  the  stone  so  that 
it  will  slope  the  proper 
amount.  The  batter  at  the 
back  of  an  abutment,  where 
it  is  hidden  by  the  earth, 
is  obtained  by  allowing  the 
ends  of  the  stones  to  pro¬ 
ject  beyond  those  above; 
the  back  ends  are  usually  left  in  the  shape  in  which  they 
come  from  the  quarry. 

111.  Undermining. — Unless  piers  or  abutments  rest 
on  solid  rock,  water  is  likely  to  wash  away  the  material  under 
them.  This  is  called  undermining,  and  is  especially  likely 
to  take  place  in  piers  placed  in  running  streams.  The  danger 
from  this  is  not  apparent,  since  the  damage  is  done  under 
water.  In  order  to  avoid  undermining,  the  pier  should  be 
carried  to  a  great  depth,  and  broken  stone  piled  up  around 
it.  This  broken  stone,  when  used  for  this  purpose,  is  called 
riprap. 


BRIDGE  DRAWING 


INTRODUCTION 

1.  The  general  principles  that  govern  the  preparation  of 
all  bridge  drawings  are  the  same  as  those  that  have  been 
explained  and  illustrated  in  Introductioyi  to  Constructio?i  Draw¬ 
ing.  In  the  present  Section,  the  additional  special  informa¬ 
tion  required  for  bridge  drawing  will  be  given,  the  application 
of  the  principles  being  illustrated  by  four  detail  drawing 
plates.  The  student  is  required  to  send  the  tracings  of  the 
drawing  plates,  one  at  a  time,  to  the  Schools  for  correction. 
He  should  retain  the  pencil  drawings  for  future  reference;  it 
may  be  necessary  for  him  to  trace  them  again. 

2.  Structural  Shapes  and  Standards. — Almost  all  the 
parts  used  in  structural  and  bridge  work  have  been  standard¬ 
ized  to  a  certain  extent,  and  their  dimensions  and  properties 
have  been  tabulated  and  printed  in  handbooks  by  the  manufac¬ 
turers  of  rolled  steel.  Bridge  draftsmen  should  have  a 
copy  of  the  handbook  used  by  the  designer.  All  the  infor¬ 
mation  of  use  to  bridge  draftsmen  that  is  usually  contained 
in  structural-steel  handbooks  is  given  in  Bridge  Tables.  The 
use  of  these  tables  is  explained  in  Bridge  Members  and 
Details ,  Parts  1  and  2.  In  preparing  the  drawing  plates, 
however,  it  will  not  be  necessary  to  consult  tables  to  any 
great  extent,  as  all  the  dimensions  required  for  the  laying 
out  of  the  work  are  shown  on  the  plates  that  he  will  receive, 
or  are  given  in  the  following  pages. 

3.  Center  Bines. — In  making  a  drawing  of  a  part  of  a 
bridge,  it  is  customary  to  draw  first  the  center  line  of  the 

COPYRIGHTED  BY  INTERNATIONAL  TEXTBOOK  COMPANY.  ALL  RIGHTS  RESERVED 

§83 


9 


BRIDGE  DRAWING 


83 


part,  and  then  refer  all  points  to  that  line.  In  addition  to 
the  first  or  main  center  line,  other  lines  are  drawn  to  repre¬ 
sent  the  centers  of  details.  For  example,  the  line  on  which 
the  centers  of  a  number  of  rivets  in  a  row  are  located  is 
drawn  before  locating  .the  rivets.  That  line  is  sometimes 
called  the  center  line  of  tlie  rivets;  more  frequently, 
however,  it  is  called  the  gauge  line.  Strictly  speaking, 
only  symmetrical  objects  have  center  lines;  but,  in  bridge 
work,  lines  that  serve  as  bases  of  reference  in  locating  details 
on  non-symmetrical  objects  are  spoken  of  as  center  lines. 
Center  lines  on  a  drawing  are  very  important,  and  should 
be  laid  out  very  accurately,  as  they  are  used  as  standards  of 
reference  from  which  to  lay  out  distances  and  locate  points. 

4.  Dimensions. — A  frequent  source  of  trouble  in  making 
a  bridge  drawing  is  the  location  of  the  dimension  lines. 
The  drawing  is  usually  so  filled  with  views  of  details  that  it 
is  difficult  to  draw  the  dimension  lines  without  interfering 
with  other  lines.  Draftsmen  should  be  very  careful  so  to 
locate  the  dimension  lines  and  write  the  dimensions  that  no 
ambiguity  can  arise.  When  there  are  several  consecutive 
dimensions,  such  as  a  number  of  rivet  spaces  that  are 

unequal,  it  is  well  to  show  them 
r  in  a  line,  so  that  they  can  be  added 
readily  when  the  drawing  is  being 

?■  checked.  In  such  a  case,  it  is  cus- 

\  * 

tomary  to  give  both  the  separate 
distances  between  rivets  and  the 
distance  between  the  end  points,  or 
between  two  easily  distinguished 
points  near  the  ends.  This  distance  is  the  sum  of  a  number 
of  smaller  distances,  and,  by  giving  it,  the  necessity  is  avoided 
of  adding  the  smaller  distances  whenever  the  total  distance  is 
wanted.  The  method  is  illustrated  in  Fig.  1,  which  represents 
the  connection  angle  at  the  end  of  a  stringer.  The  lines  a  a 
and  bb  are  the  center  lines  of  the  flange  rivets,  and  are 
2?  inches  from  the  top  and  bottom,  respectively,  of  the 
flange  angles.  The  spacing  of  the  rivets  in  the  connection 


% 


A 

l7~ 

( 

< 

) 

( 

( 

> 

< 

> 

H 

) 

V- 

<\o 

> 

-s-b 

)- 

> 

7— 

— TO 

Fig.  1 


83 


BRIDGE  DRAWING 


3 


angle  is  given  by  the  left-hand  line  of  dimensions.  For 
convenience  of  reference,  the  sum  of  all  the  dimensions  con¬ 
tained  in  the  left-hand  line  is  given  at  the  right.  This  sum 
is  the  distance  from  the  top  of  the  top  flange  angle  to  the 
bottom  of  the  bottom  flange  angle,  and  is  usually  spoken  of 
as  the  vertical  distance  back  to  back  of  the  flange  angles. 

5.  When  a  dimension  line  is  too  short  to  permit  the 
dimension  to  be  written  legibly  between  its  ends,  the  number 
indicating  the  dimension  is  placed  outside  the  line  and  close 
to  it,  as  the  dimension  of  2t  inches  at  the  top  and  bottom 
of  the  stringer  in  Fig.  1.  Dimension  numbers  should,  as  a 
rule,  be  placed  as  close  as  possible  to  the  objects  or  parts  to 
which  they  refer,  except  where,  when  so  located,  they  inter¬ 
fere  with  other  lines  or  numbers.  In  all  cases,  they  are 
located  with  respect  to  the  other  lines  or  numbers  in  such  a 
way  that  there  will  be  no  doubt  as  to  their  meaning. 

6.  Shortened  Views. — When  a  part  of  a  bridge  has  the 
same  form,  dimensions,  and  parts  for  a  considerable  dis¬ 
tance,  as  from  a  a  to  b  b}  Fig.  2,  it  is  unnecessary  to  show 
the  whole  of  it  to  scale  if  the  space  on  the  drawing  is 
limited.  In  such  a  case,  a  portion  of  the  member  may  be 
left  out,  and  the  ends  moved  closer  together.  The  parts 
that  are  then  shown  will  be  drawn  to  scale  just  as  though 
the  entire  member  were  drawn,  but  the  dimensions  referring 
to  the  omitted  or  broken  portion  are  not  shown  to  scale. 
In  Fig.  3  is  shown  the  member  shown  in  Fig.  2,  but  short¬ 
ened  so  as  to  occupy  about  one-half  the  space.  An  opening 
is  usually  left,  as  at  c,  Fig.  3,  and  lines  d ,  e  are  drawn  to  indi¬ 
cate  that  part  of  the  member  has  been  omitted.  The  cutting 
lines  are  sometimes  straight,  as  d  and  e ,  Fig.  3  ( a ),  and  some¬ 
times  irregular,  as  /  and  g,  Fig.  3  (b) .  When  a  member  is 
cut  and  shortened,  as  just  explained,  its  total  length  (13  feet 
3  inches  in  this  case)  is  written  on  a  dimension  line  between  its 
ends,  although  this  line  does  not  represent  that  length  to  scale. 

The  total  length  of  a  member  is  frequently  called  the 
over-all  dimension,  or  the  length  over  all  of  the  mem¬ 
ber.  This  dimension  should  always  be  given. 


« 


O) 


0 


E 


Cb. 


i 


jt-| — © - 


o----e- 


0 


TT 


? 

<0 

•>  i 

x 

0i 

*> 


■i 


•--©- 


<HkH-e — <h  -o 


■-©- 


ill 


\ 

*11 

**> 


*n 


,  > 


to 


)  lie 

T 

>  I1 

I1  s 

•tr 


4 


Fig. 


§83 


BRIDGE  DRAWING 


5 


7.  Representation  of  Structural  Sliapes  by  Dines. 
The  usual  methods  of  representing  structural  shapes  in 
cross-section  were  explained  and  illustrated  in  Introdiiction 
to  Construction  Drawing.  These  shapes  are  represented  in 
plan  and  elevation  as  shown  in  Fig.  4,  the  curved  corners 


Fig.  4 


being  represented  by  single  lines  at  the  points  where  the 
surfaces  joined  by  the  curves  would  intersect.  For  example, 
the  curved  corners  at  a  and  b,  Fig.  4  (a),  are  represented  in 
the  elevation  by  the  line  de ,  and  the  curved  surfaces  b  and  c 
by  the  line  fg  in  the  plan.  Similarly,  in  Fig.  4  (b) ,  the  curved 
corners  at  h  h  are  represented  in  the  elevation  by  the  lines  ij ; 
those  at  k  k,  by  the  lines 
l  m  in  the  elevation  and  the 
line  n  o  in  the  plan.  When 
channels  and  I  beams  are 
drawn  to  a  small  scale,  the 
lines  ij  and  l  m  are  very 
close  together,  and  it  is 
customary  to  draw  but  one 

line  to  represent  both  corners,  this  line  being  about  midway 
between  the  two,  as  shown  in  Fig.  5. 


8.  Cross-Sections  of  Thin  Shapes. — When  shapes 
appear  very  thin  on  drawings,  they  are  not  section-lined  or 
cross-latched  as  explained  in  Introduction  to  Construction 
Drawing ,  but  are  filled  in  solid  black,  as  shown  in  Figs.  4 
and  5.  When  two  surfaces  are  in  contact,  a  narrow  space  is 

135—32 


BRIDGE  DRAWING 


8 


Fig.  6 


Conventional  Signs  for  Structural  Rivets 


Shop 

Field 

Two  full  heads . 

O 

e 

Countersunk  inside  and  chipped . 

0 

<§> 

Countersunk  outside  and  chipped  .... 

Q 

m 

Countersunk  both  sides  and  chipped  .  .  . 

0 

m 

-  Inside 

Outside 

Both 

Sides 

Flatten  to  i  inch  high  or  counter¬ 
sunk  and  not  chipped . 


Flatten  to  i  inch  high 


0 

(B 


Flatten  to  f  inch  high 


oo 

Of 

0# 


Fig.  7 


83 


BRIDGE  DRAWING 


7 


left  between  them,  as  shown  in  Fig.  6.  This  method  of 
showing  cross-sections  is  employed  on  almost  all  drawings 
made  to  a  scale  of  1  inch  to  the  foot  or  to  a  smaller  scale. 

9.  Conventional  Signs  for  Rivets. — The  two  conven¬ 
tional  signs  for  rivets  are  explained  in  Bridge  Membei's  and 
Details ,  Part  1,  and  illustrated  in  Bridge  Tables.  The 
Osborne  standard  is  believed  to  be  the  simpler  and  plainer, 
and  will  be  used  in  the  drawing 

a 

plates  of  this  Section.  For 


venience,  the  conventional 


are  repeated  in  Fig.  7.  In  riveted 

members,  rivets  are  shown  only  in  IG'  8 

those  views  in  which  they  appear  in  end  elevation,  except 

where  but  one  view  of  the  member  is  shown,  in  which 

case  some  of  the  rivets  may  be  shown  in  side  elevation,  as 

at  a,  a ,  Fig.  8. 

10.  Eyebar  Heads. — Usually,  the  sizes  of  heads  of  eye- 
bars  are  not  given  on  bridge  drawings,  but  they  are  drawn 
to  scale.  For  this  purpose,  the  diameter  of  the  circular  head 
is  taken  from  a  table,  and  the  head  is  laid  out  as  explained  in 


Bitroduction  to  Constric¬ 
tion  Drawing .  The 
radius  of  the  curves 


that  join  the  outline  of 
the  head  with  the  sides 
of  the  bar  is  usually 
equal  to  twice  that  of 
the  circular  head,  as 
illustrated  in  Fig.  9. 


1 1 .  Pin  Nuts. 

The  long  diameter  of 
each  pin  nut  can  be 


Fig.  9 


taken  from  a  table.  The  outlines  of  these  nuts  are  drawn 
by  inscribing  hexagons  in  circles  having  diameters  equal 
to  the  long  diameters  of  the  respective  nuts.  The  thick¬ 
nesses  and  other  necessary  dimensions  are  also  taken  from 
tables. 


8 


BRIDGE  DRAWING 


§83 


12.  Numbering  Drawings. — There  are  various  sys¬ 
tems  in  use  for  numbering  detail  and  working  drawings.  In 
some  offices,  each  drawing  is  given  a  separate  number,  as 
was  done  in  Introduction  to  Constructio?i  Drawing  and  Con¬ 
struction  Drawing.  In  other  offices,  each  “job”  or  contract 
is  numbered,  and  all  drawings  relating  to  that  contract  are 
given  the  same  number.  When  this  system  is  followed,  there 
is  usually  given  a  secondary  set  of  numbers  indicating  the  num¬ 
ber  of  each  drawing  and  the  number  of  drawings  that  relate 
to  the  contract.  The  form  used  in  some  offices  is  as  follows: 

Contract  976 
Sheet  3  of  6  sheets 
and  in  others,  as  follows: 

Contract  976:  (5)  of 

In  each  case,  the  notation  indicates  that  the  drawing  is 

one  of  a  set  of  drawings  that  relate  to  contract  976,  that 

« 

it  is  drawing  number  3  of  such  set,  and  that  the  complete  set 
consists  of  six  sheets  or  drawings.  The  former  system  will 
be  used  in  the  plates  in  this  Section. 


DRAWING  PLATES 


GENERAL  CONSIDERATIONS 

13.  The  drawing  in  this  Section  consists  of  four  bridge 
plates  showing  all  the  joints  on  one  side  of  the  center  of  the 
pin-connected  truss  treated  in  Desig?i  of  a  Highway  Truss 
Bridge ,  Parts  1  and  2.  The  details  of  the  ends  of  all  the 
members  that  connect  at  the  joints  are  also  given,  together 
with  the  side  elevation  of  an  intermediate  floorbeam  and 
sidewalk  bracket.  The  student  is  advised  not  to  start  the 
drawing  of  these  plates  until  after  he  has  completed  the 
two  Sections  mentioned. 

14.  In  making  a  drawing  of  a  bridge  of  this  kind,  it  is 
the  usual  practice  to  lay  out  on  a  large  sheet  the  skeleton 
drawing  of  one-half  of  the  truss  to  a  scale  of  7,  i,  or  \  inch 


83 


BRIDGE  DRAWING 


9 


to  the  foot.  This  gives  the  directions  of  the  members  that 
meet  at  each  joint,  and  shows  the  joints  and  members  in 
their  relative  positions.  The  appearance  of  the  drawing 
when  the  skeleton  outline  has  been  drawn  is  shown  in 
Fig.  10,  in  which  fghi  is  the  border  of  the  sheet,  and 
ciB  Ee  the  outline  of  one-half  of  the  truss.  The  details  of 
the  ends  of  the  members  are  then  drawn  at  the  joints,  and 
the  members  broken  between  the  joints  to  indicate  that  por¬ 
tions  are  omitted.  The  details  of  the  members  are  usually 
drawn  to  a  scale  of 
!  or  1  inch  to  the 
foot.  Each  office  or 
drafting  room  has  a 
rule  as  to  the  scale 
to  be  used.  In  the 
following  drawing 
plates,  the  distances 
between  the  joints  are 
drawn  to  a  scale  of 
f  inch  to  the  foot,  and 
the  details  of  the  ends  of  the  members  are  drawn  to  a  scale 
of  1  inch  to  the  foot. 

In  explaining  the  layouts  of  the  following  plates,  some  of 
the  dimensions  given  in  the  text  refer  to  sizes  of  parts  and 
distances  on  the  members,  which  are  to  be  laid  out  to  the 
scale  of  1  inch  to  the  foot.  Other  dimensions,  such  as  those 
referring  to  the  location  of  views  on  the  plates  are  to  be  laid 
out  full  size  on  the  drawings.  There  will  be  no  difficulty  in 
recognizing  which  dimensions  are  to  be  scaled  and  which 
are  to  be  laid  out  full  size. 

15.  On  account  of  the  difficulty  in  handling  and  mailing, 
the  Schools  have  found  it  advisable  to  limit  the  size  of 
drawing  plates  to  13  in.  X  17  in.  inside  the  border  lines.  It 
is  impossible  to  draw  an  entire  half  truss  on  a  sheet  of  this 
size  without  using  an  inconveniently  small  scale;  hence,  to 
conform  to  the  size  of  the  plate  and  the  usual  scale,  the 
truss  is  shown  on  four  plates.  The  sheet  shown  in  Fig.  10 


10 


BRIDGE  DRAWING 


83 


may  be  considered  to  be  divided  by  the  lines  K K  and  LL , 
and  the  part  of  the  truss  in  each  of  the  four  corners  drawn  on 
a  separate  sheet. 

16.  Erection  Diagram. — When  a  truss  is  too  large  to 
be  conveniently  shown  on  a  sheet,  as  just  described,  each 
member  is  drawn  separately,  and  in  the  lower  right-hand 
corner  of  the  sheet  is  placed  a  skeleton  drawing  of  the  truss 


to  a  very  small  scale.  Each  member  is  given  a  letter  and 
number  so  as  to  show  its  position  in  the  assembled  truss. 
The  general  arrangement  of  the  views  on  such  a  drawing  is 
illustrated  in  Fig.  11.  In  most  cases,  however,  more  than 
one  sheet  is  required  in  order  to  show  all  the  members. 

17.  General  Directions. — The  plates  will  all  be  13  in. 
X  17  in.  inside  the  border  lines,  with  the  views  arranged  as 
explained  in  detail  in  the  following  articles.  A  space  of 
I2  in.  X  4  in.  is  reserved  in  each  plate  for  the  title,  but  it  is 
not  always  possible  to  locate  the  titles  at  the  lower  right- 
hand  corners  of  the  sheets.  They  are  located  either  on  the 
lower  or  on  the  right-hand  border  line. 

All  the  information  necessary  for  the  drawing  of  the  plates 
is  given  in  detail  in  the  following  articles.  When  the  distance 


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83 


BRIDGE  DRAWING 


11 


from  the  edge  of  a  piece  to  the  last  rivet  is  not  given  on  the 
plate,  it  may  in  general  be  taken  as  I2  inches.  In  case  any 
difficulty  is  experienced  in  finding  the  dimensions  of  a  section 
in  the  text  or  on  the  plate,  they  can  be  found  in  Bridge  Tables. 

The  heads  of  the  shop  rivets  on  the  plates  are  li  inches  in 
diameter,  and  the  holes  for  the  field  rivets  are  El  inch  in 
diameter.  The  letters  in  the  title  are  i  inch  in  height,  and 
all  the  other  lettering  on  the  sheets  is  -32  inch  in  height,  made 
as  described  in  Introduction  to  Construction  Drawhig. 


DRAWING  PLATE  107,  TITLE:  HIGHWAY-BRIDGE 

DETAILS 

18.  This  plate  shows  the  elevation  of  the  joint  at  the 
left  end  of  the  bottom  chord  and  two  joints  to  the  right  of  it. 
In  addition,  it  shows  side  elevations  of  the  two  verticals, 
cross-sections  of  the  two  verticals  and  end  post,  and  a  plan 
of  the  bottom  chord  members.  The  border  lines  enclose  an 
area  of  13  in.  X  17  in. 

19.  Center  Lines  of  Members. — The  center  lines  of 
the  members  are  drawn  first.  The  center  line  of  the  lower 
chord  in  elevation  is  drawn  parallel  to  and  82  inches  from  the 
top  border  line.  The  center  of  the  end  joint  is  then  located 
on  this  center  line  1  inch  from  the  left  border  line,  and  the 
centers  of  the  other  joints  are  located  from  the  first  by  laying 
off  two  distances  of  20  feet  each  to  the  scale  of  f  inch  to  the 
foot.  The  joints  will  be  referred  to  by  the  letters  given  in 
Fig.  10,  the  three  joints  on  this  plate  being  a ,  b,  and  c.  Next, 
draw  vertical  lines  through  a ,  b,  and  c,  to  represent  the  cen¬ 
ters  of  the  chair  at  a  and  the  verticals  at  b  and  c.  Next,  lay 
out  the  center  line  of  the  end  post  from  a ,  and  the  center 
line  of  the  diagonal  from  c.  There  are  various  methods  of 
specifying  the  slope  of  a  diagonal  line  on  a  bridge  drawing; 
the  most  common  is  to  give  the  coordinates  of  a  point  on  the 
line  with  reference  to  the  joint  from  which  it  starts,  or  to 
give  the  lengths  of  the  sides  of  a  right  triangle  of  which  the 
diagonal  or  part  of  it  is  the  hypotenuse.  See  Fig.  12.  The 


12 


BRIDGE  DRAWING 


83 


slope  of  a  line,  when  given  in  this  way,  is  called  the  skew. 
In  Fig.  12  ( a ),  the  total  distance  passed  over  vertically  and 
horizontally  by  a  diagonal  of  the  truss  under  consideration 
is  given;  this  method  is  convenient  and  well  adapted  to 
detail  drawings.  For  shop  drawings,  the  method  shown  in 
Fig.  12  ( b )  is  preferable;  this  gives  the  distance  passed 


Pig.  12 


horizontally  in  1  foot  vertical.  It  is  preferred  by  some  to 
give  the  skew  in  2  feet  instead  of  in  1,  since  the  workmen 
use  steel  squares  2  feet  on  a  side.  The  skew  in  2  feet,  in 
this  case,  is  M  X  24  =  17fi  inches.  Since,  in  this  case,  the 
skew  is  given  in  terms  of  the  total  distances,  it  is  best  to 
measure  along  ab  and  bc>  Fig.  13,  and  lay  off  a  a'  and  cc\ 
each  equal  to  20  feet,  to  a  convenient  scale,  say  s  inch  to  the 


foot.  Then,  erect  perpendiculars  at  ar  and  c'  and  lay  off  a '  a" 
and  cf  c",  equal  to  27  feet,  to  the  same  scale  as  a  a1  and  cc'. 
Then,  a  a"  and  cc"  are  the  center  lines  of  the  inclined  mem¬ 
bers.  When,  on  the  following  plates,  the  right  triangle 
giving  the  skew  is  drawn,  the  long  leg  of  the  right  angle 
will  in  every  case  be  made  1  inch  in  length. 


83 


BRIDGE  DRAWING 


13  . 

20.  Joint  a . — Next,  lay  off  the  width  of  the  eyebar  that 
runs  from  a  to  the  right,  6  inches  wide,  one-half  above  and 
one-half  below  the  center  line,  and  break  it  off  about  4f  inches 
from  a.  Now,  lay  off  the  top  and  bottom  of  the  angle  that 
shows  dotted  inside  the  eyebar;  this  leg  is  2i  inches  wide, 
If  inches  of  which  is  above  the  center  line.  The  left  end  of 
the  angle  is  1  foot  If  inches  and  the  first  rivet  is  1  foot 
3  inches  from  a;  the  rivets  are  6  inches  apart.  It  is  not 
necessary  to  make  circles  for  the  rivets  on  the  pencil  draw¬ 
ings,  but  simply  to  indicate  their  centers  by  short  lines  at 
right  angles  to  the  gauge  lines. 

The  head  of  the  eyebar  can  now  be  drawn.  In  Bridge 
Tables ,  the  radius  of  this  head  is  given  as  6f  inches.  Then, 
the  radius  of  the  curves  joining  the  head  to  the  straight  portion 
is  132"  inches.  The  long  diameter  of  the  nut  is  7i  inches;  the 
diameter  of  the  pin  is  4f  inches;  and  the  diameter  of  the 
threaded  end  of  the  pin  is  4.inches.  These  can  now  be  drawn. 

21.  Next,  lay  out  the  outlines  of  the  end  post,  breaking 
it  off  about  6f  inches  above  the  pin.  First,  lay  off  the  top 
and  bottom  lines  7f  and  7i  inches,  respectively,  from  the 
center  line,  and  draw  them  parallel  to  it.  Next,  lay  out 
the  thicknesses  of  the  outstanding  legs,  and  draw  the  inside 
lines  of  the  angles.  Next,  measure  7i  inches  below  the 
center  of  the  pin,  and  draw  the  end  line  of  the  end  post  to 
its  intersection  with  the  center  line.  Then,  draw  the  other 
line  at  the  end  of  the  post,  making  the  same  angle  with  the 
center  line  as  the  first  line.  Measure  in  3|  inches  from 
each  side  of  the  post  to  locate'the  edges  of  the  flange  angles, 
and  draw  them  parallel  to  the  center  line.  Next,  draw  two 
lines  very  close  to  the  edges  of  the  angles  and  parallel  to 
them,  to  represent  the  edges  of  the  8-inch  side  plate.  Now, 
lay  off  the  gauge  lines  of  the  rivets,  and  put  in  the  rivets 
according  to  the  dimensions  given  in  the  drawing.  The 
ends  of  the  tie-plates  that  appear  on  the  sides  of  the  end 
post  can  be  located  by  measuring  from  the  nearest  rivets. 

22.  Measure  up  4  inches  on  a  vertical  through  a ,  and 
draw  the  end  of  the  end  post  as  shown  on  the  drawing  plate, 


14 


BRIDGE  DRAWING 


83 


breaking  it  off  4  inches  from  the  center  of  the  pinhole. 
This  is  shown  by  itself  to  avoid  confusion  with  the  pin  nut 
and  eyebar  head.  The  top  of  the  chair  is  1  foot  8  inches 
above  the  center  of  the  pin,  and  9  inches  wide.  The  outside 
of  the  gusset  at  the  left  is  straight  from  the  outer  corner  of 
the  flange  angle  of  the  end  post  to  the  outer  corner  of  the 
chair.  The  angles  of  the  diaphragm  inside  the  gussets  are 
ih  inch  apart,  and  have  the  3-inch  leg  in  view.  The  other 
dimensions  can  be  scaled  as  given.  Some  of  the  rivets  in 
the  end  post  are  countersunk  on  one  or  both  sides  to  give 
room  for  the  eyebar  head  on  the  outside  and  the  pedestal 
on  the  inside. 

23.  Next,  locate  the  center  of  the  cross-section  of  the 
end  post  8f  inches  (on  the  inclined  center  line)  from  the 
center  of  the  pin,  and  lay  out,  according  to  the  dimensions 
given,  first  the  webs  15  in.  X  in.,  then  the  flange  angles 
3l  in.  X  3i  in.  X  I  in.,  and  then  the  side  plates  8  in.  X  1  in. 

24.  Joint  b. — Now,  draw  the  eyebars,  eyebar  heads,  pin 
and  pin  nut,  and  angles  inside  the  eyebars  at  the  joint  b,  in 
the  same  way  as  for  joint  a ;  the  dimensions  are  the  same. 
Next,  draw  the  vertical  lines  representing  the  angles  in  the 
hip  vertical,  starting  them  2f  inches  (to  scale)  above  the 
center  of  the  pin  and  breaking  them  off  62  inches  above. 
The  adjacent  backs  of  the  angles  are  inch  apart;  the  out¬ 
standing  legs  are  7 ins  inches  apart.  The  gauge  lines  for  the 
rivets  and  rivet  holes  are  4-re  inches  apart,  2 3V  inches  on 
each  side  of  the  center.  The  rivet  spacing  is  given  at  the 
left  of  the  member.  The  pin  plate  at  the  lower  end  of  this 
vertical  extends  5  inches  below  the  pin,  and  is  10  inches 
wide  at  the  bottom.  The  top  of  the  pin  plate  is  lOf  inches 
above  the  center  of  the  pin.  Next,  put  in  the  cross-section 
of  this  member,  locating  its  center  7i  inches  above  the 
center  of  the  pin,  and  make  the  angles  3iin.  X  2lin.  X  ns  in. 

25.  Next,  draw  the  side  view  of  this  vertical,  locating  its 
center  line  2i  inches  from  that  of  the  other  view,  and  break¬ 
ing  it  off  about  7  inches  above  the  center  line  of  the  bottom 
chord.  This  view  is  71  inches  wide;  the  legs  of  the  angles 


§83 


BRIDGE  DRAWING 


15  * 

are  2\  inches  wide;  and  the  gauge  lines  of  the  rivets  are 

4k  inches  apart.  At  the  lower  end  of  this  member,  the 

* 

angles  are  connected  by  a  web-plate,  which  extends  up  to 
4  feet  10  inches  above  the  center  of  the  lower  chord,  and  is 
connected  to  the  angles  by  means  of  rivets  spaced  as  shown. 
Near  the  bottom  of  the  member,  a  short  horizontal  angle 
2  k  inches  wide  is  riveted  to  the  inside  of  the  member.  Above 
the  web-plate,  the  angles  are  connected  by  latticing.  This 
latticing  is  drawn  by  first  locating  the  centers  of  the  rivets 
in  the  ends  of  the  lattice  bars  from  the  dimensions  given, 
then  drawing  the  center  lines  of  the  lattice  bars,  then  draw¬ 
ing  a  semicircle  2\  inches  in  diameter  at  the  end  of  each 
bar  and  connecting  these  semicircles  by  lines  parallel  to  the 
center  lines  and  Is  inches  from  them  on  each  side. 

26.  The  outstanding  legs  of  the  angles  are  blacked  in 
at  intervals  in  this  view  to  indicate  that  there  are  rivet  holes 
in  them.  Those  at  the  left  of  the  view  can  be  located  by 
projecting  across  from  the  front  view  shown  directly  over 
the  pin.  In  the  right-hand  side,  the  lower  rivet  is  1  foot 
7i  inches  above  the  center  line  of  the  lower  chord,  and  above 
this  there  are  eight  spaces  of  3k  inches  each.  It  is  not 
customary  to  show  rivet  holes  in  this  way  wherever  they 
occur,  but  only  when  it  is  desired  to  emphasize  some  special 
feature.  In  the  present  case,  this  view  shows  that  the  holes 
are  not  spaced  the  same  on  both  sides  of  the  truss. 

27.  Joint  c» — The  details  of  the  members  meeting  at 
the  joint  c  are  next  drawn.  The  eyebar  that  starts  toward 
joint  b  is  the  same  as  the  eyebars  at  that  joint.  The  eyebar 
that  extends  toward  the  right  is  5  inches  in  depth,  and  the 
circular  portion  of  the  head  is  6i  inches  in  radius.  The  eye- 
bar  that  is  shown  as  the  diagonal  is  6  inches  wide,  and  the 
circular  part  of  the  head  has  a  radius  of  6f  inches.  The  pin 
and  pin  nut  at  this  joint  are  the  same  as  at  joints  a  and  b. 

28.  The  vertical  shown  in  this  view  is  composed  of  two 
channels  10  inches  in  width,  extending  from  5  inches  (to 
scale)  below  the  center  of  the  lower  chord  to  about  3k  inches 
above  it.  The  tie-plates  that  show  on  the  sides  of  this  view 


16 


BRIDGE  DRAWING 


§83 


near  the  top  are  located  by  projecting  across  from  the  side 
view,  which  will  be  explained  presently.  The  inside  lines 
of  the  angles  that  are  shown  in  dotted  lines  are  A  inch  apart, 
and  the  outer  edges  are  7~iq  inches  apart.  The  rivet  holes 
in  these  two  angles  are  located  on  gauge  lines  4 ts  inches 
apart,  their  distances  from  the  center  of  the  bottom  chord 
being  shown  on  the  right  of  the  view.  The  top  and  bottom 
lines  of  these  angles  can  also  be  located  from  the  dimen¬ 
sions,  and  also  the  angles  seen  in  end  view  below  the  angles 
just  referred  to.  Next,  put  in  the  outline  of  the  pin  plate, 
8  inches  wide,  at  the  bottom  of  the  vertical,  and  then  the 
gauge  lines  of  the  rivets,  as  given  below  the  pin.  The  rivets 
connecting  the  pin  plate  to  the  channel  are  next  located. 
These  rivets  are  shown  dotted  where  they  are  hidden  by  the 
eyebar  heads;  they  are  also  shown  flattened  to  a  height  of 
f  inch  on  the  outside  of  the  member,  to  allow  the  eyebars  to 
lie  closer  to  the  vertical. 

The  cross-section  of  this  member  can  now  be  drawn  above 
the  front  elevation;  the  center  of  the  cross-section  is  7i  inches 
above  the  center  line  of  the  lower  chord.  The  channels  are 
82  inches  back  to  back,  and  the  flanges  are  2f  inches  in  width. 
On  the  inside  of  the  section  is  shown  the  outline  of  the  dia¬ 
phragm  that  is  inserted  between  the  channels  near  the  lower 
end.  The  web  of  this  diaphragm  is  -re  inch  thick.  The  legs 
of  the  angles  next  to  the  web  are  2i  inches  in  width,  and  the 
legs  in  contact  with  the  channels  are  3a  inches  in  width. 

29.  The  side  elevation  of  this  vertical  is  next  drawn, 
the  center  line  being  located  parallel  to  and  2f  inches  to  the 
left  of  the  center  line  of  the  other  view.  It  is  customary  to 
show  side  views  on  the  right  of  front  elevations;  but,  in  this 
case,  there  being  no  available  room  on  the  right,  the  side 
view  is  shown  on  the  left.  The  top  of  the  side  view  is  broken 
off  7  inches  above  the  center  line  of  the  lower  chord.  The 
lattice  bars  near  the  top  of  the  view  are  drawn  in  the  same 
way  as  for  the  hip  vertical.  The  tie-plate  is  1  foot  in  height 
and  located,  as  shown,  by  the  dimension  lines  at  the  left  of 
the  side  view.  Below  the  tie-plate  there  are  no  rivets  in  the 


83 


BRIDGE  DRAWING 


17, 


flanges  of  the  channels,  so  they  are  assumed  .to  be  cut  away, 
thus  showing  the  webs  of  the  channels  in  section.  This  is 
for  the  purpose  of  showing  the  detail  of  the  diaphragm  more 
clearly;  if  the  flanges  were  hot  cut  away,  the  diaphragm 
would  be  hidden  behind  them  to  such  an  extent  as  to  obscure 
the  details.  The  legs  of  the  diaphragm  angles  that  show  in 
this  view  are  2*  inches  in  width.  The  gauge  lines  of  the 
rivets  in  the  diaphragm  are  2i  inches  on  each  side  of  the 
center  line,  and  the  rivets  are  located  on  them  as  shown  by 
the  dimensions  at  each  side.  At  the  lower  end  of  this  view, 
the  pin  plates  are  shown  in  cross-section. 

30.  Plan  of  Bottom  Cliord. — The  plan  of  the  bottom 
chord  is  shown  below  the  elevation.  The  center  line  of  the 
plan  is  parallel  to  and  If  inches  above  the  lower  border  line. 
At  joint  a ,  only  the  ends  of  the  eyebars  are  shown;  it  is 
assumed  that  the  end  post  and  pin  have  been  removed.  At 
joint  by  the  hip  vertical  is  shown  in  cross-section.  This  view 
is  broken  off  3f  inches  from  a  and  4  inches  from  b.  The 
eyebars  are  not  parallel  to  the  center  line,  but  diverge  from 
it.  The  ends,  however,  may  be  shown  parallel  as  far  as  the 
breaks,  and  then  offset,  as  shown  on  the  drawing  plate. 
This  better  illustrates  the  fact  that  the  eyebars  diverge,  and 
shows  the  direction  in  which  they  diverge.  The  two  eyebars 
that  form  each  member  are  connected  by  lattice  bars.  When 
the  divergence  is  slight,  the  gauge  lines  of  the  rivets  that 
connect  the  lattice  bars  to  the  outstanding  legs  of  the  angles 
riveted  to  the  insides  of  the  eyebars  are  made  parallel  to 
each  other  and  to  the  center  line.  This  makes  it  easy  to  get 
the  lattice  bars  all  the  same  length,  and  is  accomplished  by 
skewing  the  gauge  lines  on  the  angles.  In  this  case,  the 
gauge  line  of  each  angle  is  lil  inches  from  the  back  of 
the  angle  at  the  left  end  and  lli  inches  from  the  back 
of  the  angle  at  the  right  end;  the  difference  of  if  inch 
does  not  practically  affect  the  strength  of  the  latticing. 

The  lattice  bars  can  be  put  in  as  follows:  First,  draw  the 
gauge  lines  of  the  rivets  in  the  angles  as  shown;  then,  locate 
the  rivets  on  these  lines,  and  draw  the  center  lines  of  the 


18 


BRIDGE  DRAWING 


§83 


lattice  bars.  Then,  draw  semicircles  2i  inches  in  diameter 
at  each  rivet,  and  draw  two  lines  2i  inches  apart  and  parallel 
to  each  center  line  to  represent  the  sides  of  the  lattice  bars. 
The  appearance  of  the  two  eyebars  latticed  in  this  way  is 
shown  in  Fig-.  14  to  an  exaggerated  scale.  This  is  the  most 
satisfactory  method  of  arranging  the  latticing  between  diver¬ 
ging  eyebars.  Other  methods  require  the  bars  to  be  of 


different  lengths,  which  involves  much  more  computation 
on  the  part  of  the  draftsman  and  more  trouble  in  the  shop. 
When  the  divergence  is  greater  than  shown  on  the  drawing 
plate,  the  same  method  of  connecting  the  lattice  bars  can  be 
used,  except  that,  in  such  a  case,  it  is  necessary  to  use  wider 
angles  on  the  eyebars. 

31.  The  nuts  shown  on  the  pin  at  the  joint  b  are  li  inches 
thick  and  are  recessed  i  inch;  the  threaded  ends  of  the  pin 
are  1&  inches  in  length  at  each  end.  Between  the  inside  eye- 
bars  and  the  pin  plates  of  the  hip  vertical,  and  also  between 
the  pin  plates,  the  pin  is  shown  enclosed  in  thin  rings  or  cyl¬ 
inders.  These  are  usually  made  of  cast  iron  about  I  or  f  inch 
in  thickness,  and  of  lengths  just  sufficient  to  fill  the  spaces 
between  the  members  on  the  pin;  they  serve  the  purpose  of 
preventing  the  members  that  connect  to  the  pin  from  moving 
sidewise. 

Wherever  there  are  spaces  in  pins  to  which  members  do 
not  connect,  they  should  be  filled  with  fillers.  The  outside 
diameter  of  the  fillers  at  the  joint  b  is  inches,  and  the 
inside  diameter  is  5  inches. 

32.  On  all  bridge  drawings,  it  is  customary  to  refer  the 
center  line  of  the  chords  to  some  plane  of  reference,  such  as 
the  top  of  the  floorbeam,  the  top  of  the  floor,  or  some  other 


' 


“ 


' 


135  §  83 


. 


83 


BRIDGE  DRAWING 


19  . 


convenient  elevation.  In  the  present  case,  the  top  of  the 
floor  at  the  center  of  the  bridge  is  used,  and  is  shown  5  feet 
3i  inches  above  the  center  line  of  the  lower  chord.  This 
line  serves  to  locate  different  parts  of  the  bridge. 


DRAWING  PLATE  108,  TITLE:  HIGHWAY-BRIDGE 

DETAILS 

33.  This  plate  shows  the  elevation  of  the  center  joint  of 
the  lower  chord  and  the  joint  next  to  the  left  of  it.  Refer¬ 
ring  to  Fig.  10,  it  is  seen  that  these  joints  are  lettered  d 
and  <r.  Between  the  two  joints  is  shown  the  elevation  of  the 
end  of  each  vertical  (they  are  the  same),  to  avoid  confusion 
with  the  eyebar  heads.  At  the  right  of  the  elevation  of 
joint  e  is  shown  a  cross-section  through  the  eyebars,  and  a 
side  elevation  of  the  verticals. 

In  addition  to  the  members  of  the  truss,  there  is  shown  on 
this  plate  a  side  elevation  of  a  sidewalk  bracket,  and  a  side 
elevation  of  one-half  of  an  intermediate  floorbeam. 

34.  Center  Lines  of  Members. — The  center  line  of 
the  lower  chord  is  first  drawn  parallel  to  and  6  inches  from 
the  top  border  line.  Next,  the  center  lines  of  the  verticals 
are  put  in;  that  at  d  is  parallel  to  and  3  inches  from  the  left 
border  line;  that  at  e  is  parallel  to  that  at  d  and  20  feet  from 
it,  to  the  scale  of  f  inch  to  the  foot.  The  center  lines  of  the 
inclined  members  are  then  laid  out  as  explained  in  Art.  19. 
Having  put  in  the  center  lines  at  both  joints,  draw  the  side 
lines  of  the  straight  portions  of  the  eyebars  at  the  joint  d , 
and  then  put  in  the  outlines  of  the  heads.  The  circular  por¬ 
tions  of  the  heads  of  the  bottom  chord  bars  and  of  the  diag¬ 
onal  at  the  left  have  a  radius  of  6|  inches;  the  radius  of 
the  curves  connecting  the  heads  to  the  straight  portions  is 
12|  inches.  The  circular  portion  of  the  head  of  the  diagonal 
on  the  right  has  a  radius  of  4}  inches;  the  radius  of  the  other 
curves  is  9  inches.  The  pin  and  pin  nut  are  the  same  as 
shown  on  the  preceding  plate;  that  is,  the  long  diameter  of 
the  nut  is  7i  inches,  the  diameter  of  the  pin  is  4l  inches,  and 
the  diameter  of  the  threaded  end  is  4  inches. 


20 


BRIDGE  DRAWING 


83 


35.  The  vertical  can  now  be  drawn.  This  view  is  9  inches 
wide,  and  is  cut  off  5f  inches  above  the  center  line  of  the 
bottom  chord;  a  space  of  1  inch  is  left  open  for  the  insertion 
of  the  cross-section,  the  center  of  which  is  2f  inches  above 
the  center  of  the  pin. 

In  spite  of  this  intermediate  break,  this  part  of  the  vertical 
is  neither  shortened  nor  lengthened.  The  spacing  at  the 
right,  8  @  3i  inches  =  2  feet  4  inches,  is  laid  out  to  the 
scale  of  1  inch  to  the  foot  in  the  same  way  as  though 
the  member  were  not  cut. 

In  the  front  elevation  of  this  vertical,  it  is  assumed  that 
the  front  side  has  been  cut  away  and  removed,  and  the 
diaphragm  between  the  channels  is  shown  in  cross-section. 
This  method  is  frequently  followed  when  the  two  faces  of  a 
member  are  not  alike,  and  serves  the  purpose  of  showing  the 
detail  of  the  opposite  side  of  the  member.  In  this  case,  this 
view  shows  the  location  and  spacing  of  the  rivet  holes  in  the 
opposite  side  of  the  member.  The  dimensions  are  laid  out 
and  the  lines  drawn  in  the  same  way  as  explained  for  the 
vertical  at  c  in  the  preceding  plate. 

36.  Joint  e. — The  members  at  <?,  the  center  joint  of  the 
truss,  can  next  be  drawn.  The  eyebars,  eyebar  heads,  pin 
nut,  and  pin  are  the  same  here  as  at  the  preceding  joint, 
except  that  one  inclined  eyebar  is  3  inches  wide  instead  of 
5  inches. 

The  vertical  is  cut  off  5f  inches  above  the  pin,  and  a  space 
1  inch  wide  is  left  open  for  the  cross-section,  the  center  of 
which  is  2f  inches  above  the  pin.  This  vertical  is  the  same 
as  that  at  d ,  but  a  different  view  is  shown;  in  this  case,  the 
front  elevation  is  shown,  and  no  part  of  the  front  face  is 
assumed  to  be  cut  away.  No  difficulty  should  be  experi¬ 
enced  in  drawing  this  view. 

37.  The  triangular  upper  part  of  the  pin  plates  at  d  and  e 
are  shown  dotted,  and  the  rivets  also  are  shown  in  connection 
with  the  remainder  of  the  members  at  the  joints.  To  avoid 
confusion,  however,  a  separate  drawing  is  made,  showing 
the  rivet  spacing  in  this  pin  plate.  For  this  purpose,  the 


§83 


BRIDGE  DRAWING 


21 


center  line  of  the  vertical  is  located  6  inches  from  the  left 
border  line,  the  center  of  the  pinhole  is  located  \\  inches 

i 

above  the  center  line  of  the  lower  chord,  and  the  view  is 
broken  off  4  inches  above  this  center  line.  The  pin  plate, 
which  is  7  inches  wide,  and  the  rivets  are  then  located 
according  to  the  dimensions  given.  The  rivets  are  shown 
flattened  to  f  inch  in  height  on  the  outside  of  the  member. 

38.  Having  completed  the  drawing  of  the  front  elevation 
of  these  two  joints,  the  side  elevation  of  the  verticals,  shown 
at  the  right  end  of  the  plate,  can  be  drawn.  The  two 
verticals  are  the  same,  so  that  one  view  serves  for  both. 
The  vertical  center  line  of  this  view  is  3i  inches  from  the 
right  border  line.  This  view  is  similar  to  the  side  view  at 
the  joint  c  in  the  preceding  plate,  except  that  the  flanges  of 
the  channels  are  not  cut  away,  and  the  pin  at  the  lower  end 
of  the  vertical,  together  with  the  eyebars  that  connect  to  it, 
are  shown.  That  part  of  the  diaphragm,  as  well  as  the 
rivets  that  are  hidden  by  the  flanges  of  the  channels,  is 
shown  in  dotted  lines.  The  vertical  is  broken  off  5f  inches 
above  the  center  of  the  pin.  The  student  should  have  no 
difficulty  in  drawing  this  view  of  the  vertical  by  following 
the  dimensions  given  on  the  drawing. 

39.  When  the  vertical  has  been  drawn,  the  eyebars  can 
be  put  in.  First,  leave  a  space  of  tV  inch  on  each  side  of 
the  vertical  to  allow  for  the  flattened  rivet  heads  and  clear¬ 
ance;  then,  lay  out  a  width  of  if  inch;  then,  one  of  \\  inch, 
then,  one  of  if  inch  on  each  side,  to  allow  for  the  thicknesses 
of  the  diagonal  eyebars  and  the  clearance  between  them. 
The  bottoms  of  these  four  bars  are  shown  4 \  inches  below 
the  center  of  the  chord;  the  tops  are  1  and  If  inches,  respect¬ 
ively,  above  the  center  of  the  chord.  The  two  inside  bars 
are  shown  in  cross-section.  Next,  lay  off  four  bars,  ItV  inch 
in  width  on  each  side  of  the  vertical,  leaving  a  space  tV  inch 
wide  between  each  two  bars.  The  heads  of  these  bars  are 
all  shown  122  inches  in  height,  and  two  of  the  bars  on  each 
side  are  shown  in  cross-section  5  inches  in  height.  The  pin, 
4f  inch  in  diameter,  pin  nuts,  li  inches  thick  with  recesses 

135—33 


22  BRIDGE  DRAWING  §83 

i  inch  deep,  and  filling-  washer  inside  the  vertical,  6i  inches 
in  diameter,  can  now  be  drawn. 

The  line  representing  the  top  of  the  floor  at  the  center  of 
the  bridge  can  now  be  put  in. 

40.  Sidewalk  Bracket  and  Floorbeam. — The  views 
at  the  bottom  of  the  drawing  plate  are  side  elevations  of  the 
intermediate  sidewalk  bracket  and  floorbeam  shown  in  their 
relative  positions.  The  center  line  of  the  truss  is  shown 
between  the  two  views,  apd  is  located  87  inches  from  the 
left  border  line.  The  top  of  the  bracket  and  floorbeam  is 
horizontal,  and  is  located  Ak  inches  above  the  bottom  border 
line.  The  right  line  of  the  bracket  is  4i  inches  from  and 
parallel  to  the  center  line  of  the  truss,  and  the  bracket  is 

3  feet  64  inches  deep  at  that  point.  At  a  point  7  feet  to  the 
left  of  the  center  line  of  the  truss,  the  bracket  is  12  inches 
deep.  By  plotting  two  points  at  these  places,  the  bottom 
line  of  the  bracket  can  be  drawn.  The  left  end  can  then  be 
drawn  parallel  to  the  center  line  of  the  truss  and  7  feet 
3f  inches  to  the  left  of  it.  Next,  draw  the  lines  representing 
the  inner  surfaces  of  the  outstanding  legs  of  the  flange 
angles,  then  the  gauge  lines  of  the  rivets  in  the  flange 
angles  If  inches  from  the  backs,  and  then  the  inner  edges 
of  the  flange  angles,  2k  inches  from  the  backs.  Then,  draw 
the  two  stiffeners,  making  them  2k  inches  wide,  with  the  out¬ 
standing  legs  at  the  left,  and  the  backs  1  foot  3  inches  and 

4  foot  3  inches,  respectively,  from  the  center  line  of  the 
truss.  The  bottoms  of  these  stiffeners  are  1  foot  2f  inches 
below  the  top  line  of  the  bracket. 

Next,  the  connection  angle  can  be  drawn  at  the  right  end 
of  the  bracket.  The  leg  that  shows  in  this  view  is  3  inches 
wide,  and  the  gauge  line  is  If  inches  from  the  right  side  of 
the  angle.  When  the  outlines  and  gauge  lines  have  all  been 
drawn,  the  rivets  and  rivet  holes  can  be  located  according  to 
the  dimensions  given  on  the  drawing  plate.  The  outstand¬ 
ing  leg  of  the  connection  angle  at  the  right  end  of  the  bracket 
is  blacked  in  at  intervals,  to  represent  the  rivet  holes  for  the 
rivets  that  connect  this  member  to  the  vertical  of  the  truss. 


BRIDGE  DRAWING 


23 


41.  The  space  remaining  on  the  drawing  plate  is  too 
small  to  show  every  part  of  the  floorbeam  to  scale,  so  it  is 
necessary  to  break  and  shorten  the  beam.  In  this  case,  it  is 
inadvisable  to  leave  out  one  large  portion,  as  then  it  would  be 
necessary  to  omit  one  or  more  of  the  stringer  connections, 
which  it  is  very  important  to  show.  The  shortening  is 
accomplished  by  omitting  a  short  section  between  each  two 
consecutive  stringer  connections.  The  left  end  of  the  floor- 
beam  is  first  drawn  4i  inches  from  the  center  line  of  the 
truss;  then,  the  bottom  line  of  the  bottom  flange  is  drawn 
parallel  to  the  top  line  and  3  feet  6i  inches  from  it.  Next, 
the  centers  of  the  stringer  connections  are  put  in,  If  inches, 
3i  inches,  4i  inches,  51  inches,  and  7f  inches,  respectively, 
from  the  center  line  of  the  truss.  Half  way  between  each 
two  consecutive  stringer  connections,  two  irregular  lines, 
about  1  inch  apart,  are  drawn  vertically  from  the  top  to  the 
bottom  lines.  An  irregular  line  is  also  drawn  f  inch  from 
the  right  border  line,  to  indicate  the  end  of  the  view. 

Next,  the  horizontal  lines  representing  the  inner  surfaces, 
the  gauge  lines,  and  the  inner  edges  of  the  top  and  bottom 
flange  angles  are  drawn,  and  the  flange  rivets  are  located  on 
the  gauge  lines  according  to  the  dimensions  given  at  the  top 
of  the  view.  The  connection  angles  at  the  left  end  of  the 
floorbeam  are  next  drawn  3f  inches  wide,  with  the  gauge 
line  2  inches  from  the  back  and  the  top  and  bottom  ends  of 
the  angles  i  inch  from  the  flange  angles;  the  rivets  are 
located  on  the  gauge  line  according  to  the  dimensions  shown 
at  the  right  of  the  connection  angle. 

Next,  the  open  holes  for  the  stringer  connections  are 
located,  by  the  dimensions  given,  from  the  center  lines  of 
the  connections  and  the  top  of  the  top  flange.  The  shelf 
angles  and  stiffeners  are  next  put  in,  the  same  procedure 
being  followed  for  each  of  them.  First,  locate  the  top  of  the 
shelf  angle  by  the  given  distance  from  the  top  of  the  top 
flange  angles,  and  draw  the  shelf  angle  3  inches  deep  and 
6  inches  long,  one-half  on  each  side  of  the  center  line. 
Next,  draw  in  the  stiffener,  placing  the  back  of  the  angle 
even  with  the  center  line  of  the  connection,  and  measuring 


24 


BRIDGE  DRAWING 


§83 


2\  inches  to  the  right  to  locate  the  right  edge.  Then,  put  in 
the  gauge  lines  of  the  shelf  and  the  stiffener  angles,  and 
locate  the  rivets  on  them  according  to  the  dimensions  given 
in  the  drawing  plate. 

The  detail  of  the  connection  of  the  bracket  to  the  floor- 
beam,  in  the  lower  left  corner,  can  now  be  drawn.  The 
center  line  of  the  bracket  and  floorbeam  is  parallel  to  and 
1|  inches  from  the  lower  border  line.  The  center  line  of  the 
vertical  is  2\  inches  from  the  left  border  line.  The  vertical 
is  composed  of  two  10-inch  channels  with  flanges  2f  inches 
in  width.  The  lines  inside  the  vertical  form  a  top  view  of 
the  diaphragm  shown  in  cross-section  in  the  upper  part  of  the 
plate.  The  top  flange  of  the  bracket  is  5-fis  inches  in  width 
and  is  broken  off  t  inch  from  the  left  border  line.  The  top 
flange  of  the  floorbeam  is  8f  inches  in  width  and  is  broken 
off  4f  inches  from  the  left  border  line.  When  the  top  flanges 
have  been  put  in,  the  connection  plates  can  be  drawn;  they 
are  8  inches  wide  with  one  edge  i  inch  from  the  back  of  a 
channel  on  each  side.  The  angles  under  the  connection 
plates  are  2\  in.  X  2l  in.  X  "Te  in.  and  are  placed  with  their 
vertical  legs  in  close  contact  with  the  flanges  of  the  channels. 
The  longitudinal  section  of  the  sidewalk  stringer  is  1  foot 
3  inches  from  the  center  of  the  vertical  and  is  lg  inch  above 
and  below  the  center  line  of  the  bracket.  The  lower  flange 
of  the  stringer  is  4|  inches  wide.  The  splice  plates  shown 
in  cross-section  are  6  inches  long.  The  rivets  can  now  be 
located  by  means  of  the  given  dimensions. 

42.  The  dimension  lines  and  dimensions  may  be  put  in 
now  on  the  whole  drawing,  or  they  may  be  put  in  on  each 
figure  as  soon  as  the  figure  is  done.  The  latter  method  is 
the  better  to  follow  on  the  pencil  drawing,  as  the  work 
is  fresh  in  the  draftsman’s  mind.  In  tracing  the  drawing, 
however,  it  is  better  to  put  in  the  dimension  lines  when 
each  view  is  traced,  and  to  put  in  the  dimensions  after  all 
lines  have  been  traced. 


.  ,  . . 


\ 


•> 


-  •  V  7  ■  * 


• * ;  .  .  .  .. 


. 

. 

. 

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ig  fltl 

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l 

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't*-* -  .  -  <, 


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135  §  83 


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■  ' 


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V 


§83  BRIDGE  DRAWING  25 

DRAWING  PRATE  109,  TITLE:  HIGHWAY-BRIDGE 

DETAILS 

43.  This  plate  shows  the  elevation  of  the  hip  joint  and 
of  the  top  chord  joint  next  to  the  right  of  it.  Cross-sections 
of  the  members  and  side  views  of  the  verticals  are  also 
shown.  In  addition,  there  is  at  the  top  of  the  plate  a  view, 
one-half  plan,  one-half  section,  of  the  top  chord,  showing  the 
connections  of  the  transverse  strut  and  of  the  diagonals  of 
the  upper  lateral  truss  to  the  top  chord. 

44.  The  elevation  and  side  views  will  be  explained  first. 
Draw  the  center  line  of  the  top  chord  parallel  to  and  5i  inches 
from  the  top  border  line.  Draw  the  center  line  of  the  hip 
vertical  parallel  to  and  4|  inches  from  the  left  border  line, 
and  the  center  line  of  the  next  vertical  parallel  to  it  and 
20  feet  i  inch  to  the  right  of  it,  to  a  scale  of  I  inch  to  the 
foot.  Draw  the  inclined  center  lines  of  the  diagonals  as 
explained  in  Art.  19.  By  reference  to  Fig.  10,  it  is  seen 
that  the  joint  on  the  left  is  joint  B,  and  that  on  the  right  is 
joint  C.  The  elevation  of  joint  B  will  be  explained  first. 

45.  When  the  center  lines  have  been  drawn,  the  top  and 
bottom  lines  of  the  top  chord  can  be  drawn  7f  and  inches, 
respectively,  above  and  below  the  center  line  of  the  chord. 
Then,  the  lines  representing  the  inner  surfaces  of  the  out¬ 
standing  legs,  the  gauge  lines  of.  the  rivets,  and  the  inner 
edges  of  the  top  and  bottom  flange  angles  can  be  drawn. 
The  top  chord  is  cut  off  at  the  left  end,  h  inch  from  a  line 
that  bisects  the  angle  between  the  center  lines  of  the  top 
chord  and  end  post;  it  is  broken  off  3|  inches  to  the  right  of 
the  center  of  the  pin.  The  intermediate  gauge  lines  are 
next  put  in  according  to  the  dimensions  at  the  right,  and  the 
rivets  in  this  part  of  the  chord  put  in  position  according  to  the 
dimensions  at  the  top  of  this  view.  Some  of  the  rivets  are 
countersunk  on  the  inside,  to  leave  room  for  the  pin  plates  on 
the  inside  of  the  end  post,  which  project  up  into  the  top  chord. 

The  pin  plates  can  now  be  drawn.  The  longest  plate  fits 
between  the  edges  of  the  flange  angles,  and  is  8  inches  wide;  it 


26 


BRIDGE  DRAWING 


83 


-p 


P/n  P/ate 


extends  li  inches  beyond  the  last  two  rivets  in  the  web.  The 
next  two  pin  plates  are  14  inches  wide,  and  fit  in  between  the 
outstanding  legs  of  the  flange  angles.  The  right  end  of  each 
plate  can  be  located  by  counting  the  rivets  enclosed  in  the 
plate.  The  left  ends  of  the  8-inch  and  the  inside  14-inch  pin 
plates  are  even  with  the  skew  end  of  the  chord;  the  outside 

pin  plate  extends  out 
&\  beyond  the  pin,  the 

vk  outline  being  as 

shown  in  Fig.  15. 
The  upper  edge  of 
the  pin  plate  is  con¬ 
tinued  parallel  to  the 
center  line  B  C  as  far 
as  its  intersection  a 
with  the  bisector  b  c. 
The  outer  edge  ad  of 
the  pin  plate  then  con¬ 
tinues  parallel  to  the  center  line  of  the  end  post  to  the  inter¬ 
section  of  ad  with  the  center  gauge  line  of  the  chord.  The 
other  edge  is  then  drawn  from  d  to  <?,  the  latter  being  ver¬ 
tically  below  a.  This  view  will  be  completed  after  the  plan 
has  been  drawn. 


A/  \ 

\  ^Gaugel/ne  ^ 

\e  \  ..  / 

J  J  ^Center Line  of  Chord 

Fig.  15 


46.  Now,  proceed  in  the  same  way  for  the  end  post  as 
for  the  top  chord  just  drawn,  and  break  it  off  4  inches  from 
the  center  of  the  pin.  First,  draw  the  flange  angles,  then  the 
8-inch  side  plate,  and  then  the  gauge  lines.  Next,  put  in  the 
rivets  according  to  the  dimensions,  and  then  draw  the  pin 
plate,  which  is  on  the  inside  of  the  member.  Some  of  these 
rivets  (those  shown  in  dotted  lines)  are  countersunk  on  both 
the  inside  and  the  outside  of  the  section,  to  allow  room  for 
the  eyebar  heads  on  the  inside,  and  for  the  projecting  pin 
plates  of  the  top  cliord  on  the  outside.  The  upper  end  of 
this  pin  plate  is  cut  off  in  the  same  way  as  that  on  the  top 
chord,  as  illustrated  in  Fig.  15.  The  portions  of  the  tie-plates 
that  show  in  this  view  can  be  located  and  drawn  as  they  are 
shown  on  the  drawing  plate.  Now,  draw  the  cross-section 


83 


BRIDGE  DRAWING 


27 


of  the  end  post,  making  its  center  line  inches  from  the 
center  of  the  pin.  In  the  cross-section,  the  clear  distance 
between  the  webs  is  Ilf  inches,  the  webs  are  15  in.  X  A  in., 
the  side  plates  are  8  in.  X  i  in.,  and  the  flange  angles  are 
3i  in.  X  3i  in.  X  i  in. 

47.  Next,  the  eyebar  that  forms  the  diagonal  can  be 
drawn.  The  bar  is  6  inches  wide,  one-half  on  each  side 
of  the  center  line,  and  the  radius  of  the  circular  part  of  the 
head  is  6f  inches.  The  diameter  of  the  pin  is  4f  inches,  that 
of  the  screw  end  3!"  inches,  and  that  of  the  nut  6f  inches. 
These  can  now  be  put  in. 

48.  The  hip  vertical  is  drawn  next.  The  pin  or  hanger 
plate  should  be  drawn  first.  This  is  10  inches  wide  from 
7  inches  above  the  pin  to  8  inches  below  it,  and  then  narrows 
to  7~re  inches  at  1  foot  91  inches  below  the  pin.  The  angles 
are  drawn  next;  their  backs  are  -ft-  inch  apart,  and  their 
outer  edges  are  7-re  inches  apart.  The  upper  ends  of  the 
angles  are  2i  inches  below  the  center  of  the  pin,  and  the 
break  at  the  lower  end  is  4i  inches  below.  The  center  of 
the  cross-section  is  5  inches  below  the  center  of  the  pin.  Of 
the  rivets  at  the  upper  end  of  the  hip  vertical,  only  those  are 
shown  that  appear  below  the  other  members.  The  rivets 
that  are  hidden  are  omitted,  as  they  would  confuse  the  draw¬ 
ing  if  shown.  In  this  case,  the  upper  end  of  the  hip  vertical 
and  the  spacing  of  the  rivets  are  shown  in  an  additional  view 
below  and  to  the  right  of  the  joint.  The  center  line  of  this 
view  is  If  inches  from  the  center  line  of  the  hip  vertical  in 
the  other  view,  and  the  center  of  the  pinhole  is  3f  inches 
below  the  center  line  of  the  top  chord.  The  three  upper  rivets 
in  this  view  are  countersunk  for  the  purpose  of  allowing  the 
eyebars  in  the  end  diagonal  to  lie  close  to  the  hanger  plates. 

49.  Next,  draw  the  side  elevation  of  the  hip  vertical 
shown  just  to  the  right  of  joint  B.  The  center  line  of  this 
view  is  4i  inches  from  the  center  of  the  pin  at  B;  the  view 
extends  down  to  5  inches  below  the  center  of  the  top  chord. 
This  view  can  be  laid  out  very  readily  by  the  dimensions 
given. 


28 


BRIDGE  DRAWING 


50.  Joint  C. — At  the  joint  C,  first  draw  the  irregular 
lines  at  the  ends  of  the  top  chord  2  inches  from  the  center 
of  the  pin  at  each  end,  and  project  all  the  necessary  lines 
across  from  joint  B.  Now,  put  in  the  rivets  according  to  the 
dimensions,  and  show  the  left  end  of  the  8-inch  side  plate 
10f  inches  from  the  center  of  the  pin.  The  rivets  around 
the  pin  are  flattened  to  f  inch  high  on  the  inside,  to  give 
room  for  the  eyebars.  Next,  draw  the  eyebars  5  inches 
wide,  and  the  eyebar  heads  with  a  radius  of  5f  inches.  The 
pin  and  nut  can  now  be  drawn.  The  diameter  of  the  pin  is 
3f  inches,  that  of  the  threaded  end  is  2f  inches,  and  that  of 
the  nut  is  5A  inches. 

51.  Next,  draw  the  vertical,  making  it  10  inches  wide 
and  cutting  it  off  3f,  4f,  and  6i  inches  below  the  center  line 
of  the  top  chord.  Draw  the  angles  that  show  in  dotted  lines, 
locating  the  top  f  inch  and  the  bottom  6 1  inches  below  the 
center  of  the  top  chord.  These  angles  are  each  3  inches 
wide,  and  their  backs  are  Ar  inch  apart.  Now,  put  in  the 
rivets  in  this  view  according  to  the  dimensions.  Next,  draw 
the  cross-section,  locating  its  lower  line  4f  inches  below  the 
center  of  the  top  chord;  The  flanges  of  these  channels  are 
2 f  inches  wide;  the  angles  are  each  3  in.  X  3  in.  X  A  in. 

52.  The  outline  of  the  pin  plate  at  the  top  of  the  vertical 
is  shown,  but  the  rivets  are  omitted  from  this  view  to  avoid 
confusion.  They  are  shown  in  a  separate  view,  the  center 
line  of  which  is  If  inches  to  the  left  of  the  center  of  the 
vertical  in  the  elevation.  The  center  of  the  pinhole  is 
2  inches  below  the  center  of  the  top  chord.  The  rivets  are 
shown  flattened  to  f  inch  in  height  to  provide  room  for  the 
eyebars. 

53.  The  side  view  of  the  vertical  at  C  is  next  drawn  on 
the  right  end  of  the  sheet,  and  the  eyebars  and  top  chord 
are  shown  in  cross-section  in  their  relative  positions. 
The  center  line  of  this  view  is  located  parallel  to  and 
If  inches  from  the  right  border  line.  The  cross-section  is 
first  drawn  in  the  same  way  as  for  the  end  post  (see 
Art.  46).  Then,  the  vertical  is  drawn  8f  inches  in  width, 


§83 


BRIDGE  DRAWING 


29 


and  the  tie-plate  and  lattice  bars  are  drawn  according  to  the 
dimensions. 

The  gauge  lines  of  the  rivets  in  the  flanges  of  the  chan¬ 
nels  are  scaled  in  position,  and  the  center  lines  of  the  lattice 
bars  are  drawn  as  explained  before.  The  lattice  bars  can 
then  be  drawn  in.  The  view  is  broken  3f,  4i,  and  6f  inches 
below  the  center  line  of  the  top  chord.  The  angles  on  the 
right  side  of  this  view  are  located  by  projecting  the  top  and 
bottom  across  from  the  dotted  lines  shown  in  the  front 
elevation;  the  rivet  holes  are  then  located  according  to  the 
dimensions.  These  angles  are  for  the  connection  of  the 
transverse  strut  to  the  vertical. 

The  cross-section  of  the  top  chord  can  now  be  drawn. 
The  pin  nuts  on  the  outside  of  this  section  are  1  inch  in 
thickness  with  recesses  f  inch  deep,  and  the  threaded  ends 
of  the  pins  project  i  inch  beyond  them  at  each  end.  The 
eyebars  forming  the  diagonal  that  connects  at  C  are  shown 
between  the  inside  surfaces  of  the  chord  section  and  the 
outside  surfaces  of  the  vertical. 

54.  Plan  of  Top  Chord. — The  plan  of  the  top  chord  is 
shown  at  the  upper  part  of  the  plate.  The  center  line  of 
this  view  is  drawn  parallel  to  and  3|  inches  from  the  top 
border  line.  The  centers  of  the  joints  are  located  by  project¬ 
ing  up  from  the  elevation.  In  the  portion  of  the  plan  shown 
below  the  center  line  of  the  chord,  it  is  assumed  that  the 
upper  flange  is  removed.  The  web  is  first  drawn  in  cross- 
section,  Te  inch  thick,  with  the  inner  line  6  inches  from  the 
center  line.  Next,  the  8-inch  side  plate  at  the  joint  C  and 
the  pin  plates  at  the  joint  B  are  shown  in  section.  Their 
ends  are  located  by  projecting  up  from  the  center  line  of  the 
elevation.  The  plan  is  broken  off  at  three  places,  each  of 
which  is  3f  inches  from  the  next  joint.  The  line  represent¬ 
ing  the  outside  surface  of  the  vertical  leg  of  the  bottom 
flange  angle  is  next  drawn,  and  then  the  gauge  line  and 
the  outer  edge  of  the  bottom  flange  angle.  The  rivets  are 
located  on  the  gauge  line  according  to  the  dimensions  given, 
and  the  tie-plates  and  lattice  bars  put  in  on  this  half  of  the 


30 


BRIDGE  DRAWING 


83 


plan.  The  ends  of  the  tie-plates  on  the  bottom  flange  in 
the  elevation  can  now  be  located  by  projecting  down  from 
the  plan. 

55.  The  upper  half  of  the  plan  is  now  drawn.  It  is  best 
first  to  draw  the  gauge  line  of  the  rivets  in  the  outstanding 
leg  of  the  flange  angle  8A  inches  from  the  center  line,  and 
to  locate  the  rivets  along  this  line  according  to  the  dimen¬ 
sions  given  on  the  plate.  Then,  the  tie-plates  and  lattice 
bars  can  be  drawn  as  shown,  and  afterwards  the  lines  repre¬ 
senting  the  web  and  vertical  leg  of  the  top  flange  angle  can 
be  drawn.  By  proceeding  in  this  way  for  both  joints,  the 
proper  parts  of  the  lines  representing  the  web  can  be  shown 
full  or  dotted  the  first  time  they  are  drawn.  The  open  holes 
in  the  plan  near  the  joint  B  are  for  the  connection  of  the 
portal  at  this  joint. 

56.  At  the  joint  C  there  is  also  shown  the  connection  of 
the  top  flange  of  a  transverse  frame  and  of  two  diagonals  of 
the  upper  lateral  truss  to  the  top  flange  of  the  top  chord. 
For  this  purpose,  the  top  tie-plate  at  this  joint,  which  is 
2  feet  9i  inches  in  width,  is  extended  out  1  foot  5ff  inches 
from  the  center  line  of  the  chord,  and  acts  as  a  gusset  or 
lateral  connection  plate.  The  center  line  of  the  transverse 
strut  is  located  by  projecting  up  from  the  elevation.  The 
top  flange  angles  of  the  transverse  strut  are  inch  apart, 
and  the  legs  shown  in  this  plan  are  each  3  inches  wide.  The 
angles  are  broken  off  2f  inches  from  the  center  line.  Next, 
the  center  lines  of  the  diagonals  are  put  in  according  to  the 
given  skew,  in  the  manner  explained  in  Art.  19.  They  are 
drawn  from  the  intersection  of  the  center  lines  of  the  chord 
and  transverse  strut.  In  the  present  case,  each  diagonal  is 
composed  of  one  angle,  the  leg  shown  in  the  plan  being 

inches  in  width.  The  angles  are  located  with  the  backs 
on  the  center  lines,  and  at  the  ends,  small  angles,  called 
lug:  angles,  help  to  transmit  the  stress  from  the  lateral 
angle  to  the  gusset.  When  there  is  no  lug  angle  on  the 
end  of  a  lateral,  the  center  of  gravity  of  the  lateral  is  usually 
made  to  coincide  with  the  center  line  drawn  on  the  sheet. 


’ 


' 

: 

' 


} 


I  ;  i ; 

■ 


- 


V*  I 


. 


'  A . •  ■  .  '  - 


■ 


, 


m  .  :  ■"$  ■  i 


tr 

RcO  , 


.  S 


*  ’•-r 


135  §83 


— 


•r  X  -  .  .  . 


i  -  .  '  ■ : 


'  ■  4VEfl£Z2f  A  if  /a 


!  *  : 


■ 


’  .  .  ,  ‘  •  ■  ' 


VT^ 


§83 


BRIDGE  DRAWING 


31 


When,  as  in  this  case,  there  is  a  lug  angle  at  the  end,  the 
center  of  gravity  of  the  lateral  angle  is  also  sometimes  made 
to  coincide  with  the  center  line  as  just  described;  but  it  is 
frequently  arranged  as  shown  in  the  plan,  the  center  line 
passing  between  the  lug  angle  and  lateral  angle  and  coinci¬ 
ding  with  the  back  of  the  latter  throughout  its  length.  The 
lateral  angles  are  shown  broken  of!  about  t  inch  from  the 
top  border  line. 

57.  The  pins  and  top  views  of  the  verticals  are  frequently 
shown  with  the  plan  of  the  top  chord.  They  are  omitted 
here  simply  to  avoid  confusion  and  unnecessary  work. 


DRAWING  PLATE  110,  TITLE:  HIGHWAY-BRIDGE 

DETAILS 

58.  In  making  a  bridge  drawing,  it  is  customary  to 
draw  the  elevation  first  and  then  the  plan  and  lateral  con¬ 
nections,  as  in  the  preceding  plate.  In  drawing  the  present 
plate,  however,  since  the  student  is  familiar  with  the  general 
arrangement  of  the  parts,  it  will  be  most  convenient  for  him 
to  draw  the  plan  first.  In  the  plan  on  this  plate,  there  is 
shown,  in  addition  to  the  detail  of  the  connection  of  the 
laterals  to  the  top  chord,  the  detail  of  the  intersection  of 
the  two  diagonals  of  the  top  lateral  truss  at  the  center  of  a 
panel,  and  also  the  angle  that  connects  this  intersection 
with  the  top  flanges  of  the  transverse  frames  near  the  center 
of  the  bridge. 

The  center  line  of  the  top  chord  is  first  drawn  parallel  to 
and  4i  inches  from  the  top  border  line.  The  panel  point 
at  D  is  then  located  4f  inches  from  the  left  border  line,  and 
that  at  E  20  feet  \  inch  from  it,  to  the  scale  of  f  inch  to 
the  foot.  Vertical  lines  are  drawn  at  these  points  to  repre¬ 
sent  the  center  lines  of  the  verticals.  The  cross-section  of 
the  web  and  pin  plates  and  the  bottom  plan  of  the  top 
chord  are  drawn  in  the  same  way  as  in  the  preceding  plate. 
The  splice  plates  shown  in  cross-section  are  2  feet  3  inches 
long,  and  their  centers  are  2  feet  6|  inches  from  the  center 


32 


BRIDGE  DRAWING 


83 


of  the  pin  at  D.  The  pin  plates  on  the  inside  of  the  chord 
at  D  and  E  are  each  2  feet  3i  inches  long.  The  remainder 
of  this  plan  can  be  drawn  according  to  the  dimensions.  It 
is  shown  broken  off  4i  inches  to  the  left  and  Si  inches  to 
the  right  of  the  center  of  the  joint  at  D ,  and  Si  inches  to  the 
left  and  right  of  the  center  of  the  joint  at  E. 

59.  Next,  the  gauge  line  of  the  rivets  in  the  top  flange 
angle  is  located  8^6  inches  above  the  center  line,  and  the 
rivets  are  located  along  this  gauge  line  according  to  the 
dimensions.  Then,  the  tie-plates  and  lattice  bars  are  put  in 
as  shown.  The  tie-plates  are  the  same  size  as  those 
described  in  Art.  56  in  connection  with  the  preceding 
plate.  The  lines  representing  the  top  flange  angle  and  the 
side  of  the  web  are  then  put  in,  completing  this  part  of 
the  view. 

60.  Next,  the  center  line  of  the  struts  that  run  from  the 
intersections  of  the  diagonals  to  the  transverse  frames  is 
drawn  parallel  to  and  i  inch  from  the  top  border  line.  The 
gauge  line  of  the  angle  is  assumed  to  coincide  with  this 
center  line;  at  the  center  of  the  panel,  two  lines  are  drawn 
at  the  proper  skew  to  represent  the  center  lines  of  the 
diagonals,  and  short  lengths  of  these  diagonals  are  drawn. 
Then,  the  ends  of  the  longitudinal  angles  are  located,  and 
the  gusset  at  the  center  of  the  panel  is  drawn  according  to 
the  given  dimensions.  The  center  lines  of  the  transverse 
struts  have  already  been  drawn,  and  the  angles  are  spaced 
equally  on  each  side  of  those  lines,  the  angles  being  inch 
apart,  and  each  being  3  inches  in  width.  These  angles  can 
now  be  drawn,  and  broken  off  about  i  inch  from  the  top 
border  line  and  about  half  way  between  the  center  line  of 
the  bridge  and  the  center  line  of  the  top  chord.  The  gussets 
at  the  centers  of  the  transverse  frames  can  now  be  drawn 
according  to  the  dimensions.  The  laterals  are  then  drawn, 
thus  finishing  the  plan. 

61.  The  center  line  of  the  top  chord  in  elevation  is 
parallel  to  and  7  inches  from  the  top  border  line.  The  cen¬ 
ter  lines  of  the  verticals  have  already  been  located.  The  top 


§83 


BRIDGE  DRAWING 


33 


chord  can  first  be  drawn  according  to  the  dimensions.  Since 
this  view  is  entirely  similar  to  views  of  the  top  chord  previ¬ 
ously  drawn,  it  is  deemed  unnecessary  to  explain  it  in  detail. 
The  views  are  broken  4i  inches  to  the  left  and  3i  inches  to 
the  right  of  the  center  of  the  pin  at  D,  and  3i  inches  to  the 
left  and  li  inches  to  the  right  of  the  center  of  the  pin  at  E. 
The  rivets  in  the  chord  near  the  pin  at  D  are  shown  counter¬ 
sunk  on  the  inside  to  leave  room  for  the  eyebar  heads. 
At  E ,  both  diagonals  are  counters  and  connect  at  the  center 
of  the  pin.  There  is  then  no  necessity  for  countersinking 
the  rivets  at  the  joint  E. 

62.  The  verticals  c&n  next  be  drawn  in  the  same  way  as 
has  been  described  several  times  in  the  preceding  articles. 
Both  verticals  are  broken  off  3f,  3f,  and  5f  inches  below 
the  center  line  of  the  top  chord.  The  top  line  of  the  angles 
shown  dotted  is  !  inch,  and  the  bottom  line  is  5i  inches, 
below  the  center  line  of  the  top  chord. 

63.  The  eyebars  can  next  be  drawn  3  inches  in  width 
and  with  circular  heads  having  a  radius  of  4  inches.  The 
pins  are  3i  inches,  the  threaded  ends  are  inches,  and  the 
pin  nut  is  51^6  inches  in  diameter.  These  can  now  be  drawn. 

64.  In  order  to  avoid  confusion  in  the  drawing,  the 
upper  end  of  the  verticals,  which  are  alike,  is  shown  by  itself, 
half  way  between  the  two  verticals  and  with  the  center  of  the 
pinhole  2  inches  below  the  center  line  of  the  top  chord.  The 
rivets  connecting  the  pin  plate  to  the  web  of  the  channel  are 
shown  flattened  on  the  outside  to  f  inch  in  height.  This  is 
necessary  at  the  joint  D  to  leave  room  for  the  eyebar  heads, 
and  is  done  at  joint  E  for  the  purpose  of  having  the  verticals 
alike. 

< 

65.  The  side  view  of  the  verticals,  showing  also  the 
cross-section  of  the  top  chord,  is  given  on  the  right-hand  end 
of  the  plate,  with  the  center  line  parallel  to  and  2  inches  from 
the  right  border  line.  This  is  so  much  like  other  side  views 
that  have  been  already  explained  in  full  that  it  is  deemed 
unnecessary  to  explain  this  view  in  detail.  The  nuts  are 


34 


BRIDGE  DRAWING 


§83 


1  inch  in  thickness,  with  recesses  f  inch  deep,  and  the 
threaded  ends  project  \  inch  at  each  end  beyond  the  outer 
surfaces  of  the  nuts.  The  two  diagonals  that  connect  at  E 
are  shown  iV  inch  apart.  The  spaces  between  their  outer 
surfaces  and  the  inner  surfaces  of  the  verticals,  and  between 
the  outer  surfaces  of  the  verticals  and  the  inner  surfaces  of 
the  chord  sections,  are  filled  with  filling  rings  5  inches  in 
diameter. 


INDEX 


Note  1. — All  items  in  this  index  refer  first  to  the  section  (see  the  Preface),  and  then 
to  the  page  of  the  section.  Thus,  “Abutment  location,  §82,  p4,”  means  that  abutment 
location  will  be  found  on  page  4  of  section  82. 

Note  2. — The  abbreviations  hb  and  rtb  in  this  index  stand,  respectively,  for  “highway 
bridge  ”  (or  “  bridges  ’’)  and  “  railroad  truss  bridge  ”  (or  “  bridges”). 


A 

Abutment  construction,  §82,  p62. 

Curved- wing,  Definition  of,  §82,  p56. 
Definition  of,  §82,  pi. 
design,  §82,  p48. 

Flaring-wing,  Definition  of,  §82,  p53. 
footings,  Design  of,  §82,  p52. 
location,  §82,  p4. 
pier,  Definition  of,  §82,  p2. 

Skew,  Definition  of,  §82,  pp4,  59. 
Straight-wing,  Definition  of,  §82.  p53. 

T,  Definition  of,  §82,  p48. 

U,  Definition  of,  §82,  p48. 

Width  of  base  of,  §82,  p51. 

Wing,  Definition  of,  §82,  pp2,  48. 
wings,  Forms  of,  §82,  p56. 
wings,  Size  of,  §82,  p56. 

wings,  Thickness  of,  §82,  p57. 

Abutments,  Batter  of,  §82,  p51. 

Calculations  for,  §82,  p62. 

Classes  of,  §82,  p48. 

Curved-wing,  Design  of,  §82,  p58. 
Estimates  for,  §82,  p6. 

Flaring-wing,  Design  of,  §82,  p57. 
for  an  I-beam  hb,  Location  of,  §76,  pi. 
Materials  used  for,  §82,  p62. 

Pedestal  blocks  for,  §82,  p51. 

Pier,  Uses  of,  §82,  p61. 

Plans  for,  §82,  p9. 

Pockets  in  bridge  seats  of,  §82,  p51. 

Skew,  Design  of,  §82,  p59. 

Specifications  for.  §82,  p64. 

Stability  of,  §82,  p62. 

Straight-wing,  Design  of,  §82,  p57. 

T,  Design  of,  §82,  p52. 

U,  Design  of,  §82,  p53. 

•  Undermining  of,  §82,  p66. 

Wing,  Types  of,  §82,  p53. 

Anchor  bolts,  Specifications  for,  §74,  pp20,  40. 


Angles,  Connection,  for  floor,  Specifications 
for,  §74,  ppl4,  45. 

Flange,  Specifications  for,  §74,  ppl6,  36. 
Reentrant,  Specifications  relating  to,  §74, 
p46. 

Single,  Specifications  relating  to,  §74, 
ppll,  31. 

Annealing,  Specifications  relating  to,  §74,  p46. 
Area  of  bearing  for  hb,  §78,  p40. 
of  bearing  for  rtb,  §79,  p61. 
of  flanges,  Calculation  of,  §75,  p6. 

Areas,  Flange,  Curve  of,  §75,  pp7,  19. 

B 

Base  of  abutment,  Width  of,  §82,  p51. 
Batter,  Frost,  of  a  parapet,  §82,  p50. 
of  a  pier,  Forming  of,  §82,  p66. 
of  abutments,  §82,  p51. 
of  an  abutment,  Forming  of,  §82,  p66. 
of  piers,  §82,  pl2. 

Beams,  Stresses  in,  §75,  pi. 

Bearing  values  of  rivets.  Specifications  rela¬ 
ting  to,  §74,  ppll,  30. 

Bearings  for  bridges,  Specifications  for  details 
of,  §74,  p20,  40,  50. 
for  hb,  Design  of,  §78,  p40. 
for  plate-girder  railroad  bridge,  §76,  p42. 
for  plate  girders,  §75,  p30. 
for  rtb,  Design  of,  §79,  p61. 

Rocker,  for  plate  girder,  §75,  p34. 
Bedplates  for  bridges,  Specifications  for,  §74, 
pp20,  40. 

for  plate  girders,  Size  of,  §75,  p30. 

Belt  course  of  a  pier,  §82,  p23. 

Bending  moment  in  pins  of  hb,  §78,  pl6. 
moment,  Maximum,  in  I-beam  railroad 
bridge,  §76,  ppl4,  15. 

Bents,  Steel  trestle,  Specifications  for,  §74, 
ppl9,  39. 


Vll 


Vlll 


INDEX 


Bids  for  bridges,  §74,  p3. 

Blocks,  Chord,  in  wooden  bridges,  §80,  p24. 
Pedestal,  for  abutments,  §82,  p51. 

Pedestal,  for  piers,  §82,  pp3,  12. 

Bolts,  Anchor,  Specifications  for,  §74, 
pp20,  40. 

Specifications  relating  to,  §74,  p48. 

Bottom  chord  of  hb,  Design  of,  §77,  p34. 
chord  of  hb,  Packing  of,  §78,  p29. 
chord  of  Howe  wooden  bridge,  §80,  p26. 
chord  of  rtb,  Design  of,  §79,  p27. 
chord  of  rtb,  Location  of  center  line  of.  §79, 
p29. 

chord  of  rtb,  Splicing  of,  §79,  p50. 

Bracing,  Lateral,  between  stringers  of  rtb, 
§79  p6. 

of  bridges.  Specifications  for,  §74,  pp21, 
41. 

Bracket  of  hb,  Sidewalk,  Connection  of,  to 
floorbeam,  §78,  pll. 

of  hb,  Sidewalk,  Connection  of,  to  truss, 
§78,  p9. 

Sidewalk,  Drawing  of,  §83,  p22. 

Brackets,  Sidewalk,  for  hb,  Design  of,  §77, 
pp20,  25. 

Sidewalk,  of  hb,  Connections  of,  §78,  p3. 
Breakers,  Ice,  for  piers,  Object  of,  §82,  p3. 
Bridge,  Combination,  §80,  pp3,  6,  35. 
crossing,  Direction  of,  §82,  p4. 
crossing,  Skew,  §82,  p4. 
data,  General  form  of,  §74,  p55. 
drawings,  Size  of,  §83,  p8. 
erection,  Specifications  relating  to,  §74, 
p52. 

Highway  (see  Highway  bridge). 

I-beam  highway,  Design  of,  §76,  pi. 

I-beam  railroad,  Design  of,  §76,  pl2. 
inspection,  Specifications  relating  to,  §74, 
p53. 

joints,  Drawing  of,  §83,  pp20,  28. 

Kingpost  (see  Kingpost). 

Kingrod  (see  Kingrod). 
location,  §74,  p56 

materials,  Shipment  of,  Specifications  for, 
§74,  p50. 

materials,  Specifications  for,  §74,  p42. 
members,  Drawing  of,  §83,  pplO,  19. 
Plate-girder  railroad,  Design  of,  §76,  pl9. 
Queenpost  (see  Queenpost) . 

Queenrod  (see  Queenrod) . 

Railroad  (see  Railroad  bridge). 
seat,  Conditions  affecting  dimensions  of, 
§82,  plO. 

-seat  course,  Definition  of,  §82,  p2. 

-seat  course,  Design  of,  §82,  p65. 

-seat,  Definition  of,  §82,  p2. 
seat,  Main,  Definition  of,  §82,  p3. 


Bridge — (Continued) 

seat  of  abutment.  Conditions  affecting 
dimensions  of,  §82,  p48. 
seat  of  abutment,  Pockets  in,  §82,  p51. 

-seat  plan  for  hb,  §78,  p45. 

-seat  plan  for  I-beam  hb,  §76,  p3. 

-seat  plan  for  rtb,  §79,  p64. 
seat,  Specifications  relating  to,  §74,  p52. 
seats  for  stringers  of  rtb,  §79,  p65. 
seats  for  trusses  of  rtb,  §79,  p64. 

Towne  lattice  (see  Towne). 
work,  Cost  of,  §82,  pp6,  7,  9. 

Bridges,  Clear  height  of,  §74,  p57. 

Early  methods  of  constructing,  §74,  pi. 
Plalf- through,  Specifications  relating  to  use 
of,  §74,  p6. 

Plans  and  proposals  for,  §74,  p3. 

Railroad,  Specifications  for  the  design  of, 
§74,  P5. 

Selection  of,  §74,  p56. 

Specifications  as  to  kinds  of,  §74,  pp5,  22. 
Specifications  for  the  construction  of,  §74, 
p42. 

Specifications  for  the  design  of,  §74,  p3. 
Weights  of,  §74.  p66. 

Width  of,  §74,  p57. 

Wooden  (see  Wooden  bridge ri. 

C 

Camber,  Specifications  relating  to,  §74, 
ppl3,  32. 

Castings,  Steel,  Specifications  relating  to,  §74, 
pp43,  50. 

Center  line  of  rtb  bottom  chord,  Location  of, 
§79,  P29. 

line  of  top  chord  of  rtb,  Location  of,  §79, 
p37. 

lines,  Use  of,  in  drawings,  §83,  pi. 
Centrifugal  force  on  bridges,  Specifications 
relating  to,  §74,  pp8,  27. 
force  on  piers,  §82,  p30. 

Chord  blocks  in  wooden  bridges,  §80,  p24. 
Bpttom,  of  hb,  Design  of,  §77,  p34. 
Bottom,  of  hb,  Packing  of,  §78,  p29. 
Bottom,  of  Howe  wooden  bridge,  §80,  p26. 
Bottom,  of  rtb,  Design  of,  §79,  p27. 
Bottom,  of  rtb,  Location  of  center  line  of, 
§79,  P29. 

Bottom,  of  rtb,  Splicing  of,  §79,  p50. 
joints  for  combination  roof  trusses,  §81, 
p48. 

joints  for  steel  roof  trusses,  §81,  p53. 
joints  for  wooden  roof  trusses,  §81,  p46. 
joints  of  combination  bridges,  §80,  pp35,  37. 
members  of  hb,  Divergence  of,  §78,  p30. 
members  of  riveted  trusses,  Specifications 
for,  §74,  ppl7,  18,  37,  38. 


INDEX 


IX 


Chord — (Continued) 

of  roof  truss,  Definition  of,  §81,  p5. 
splices  for  rtb,  Design  of,  §79,  p48. 

Top,  of  hb,  Design  of,  §77,  p39. 

Top,  of  hb,  Splices  in,  §78  pl4. 

Top,  of  hb,  Width  of,  §78,  pl7. 

Top,  of  Howe  wooden  bridge,  §80,  p26. 
Top,  of  rtb,  Design  of,  §79,  p34. 

Top,  of  rtb,  Eccentricity  of,  §79,  p37. 
Top,  of  rtb,  Splicing  of,  §79,  p48. 

Chords  of  Towne  lattice  truss,  Splices  in,  §80, 

p34. 

Clearance  diagram  for  bridge,  §74,  p57. 
in  bridges,  Specifications  relating  to,  §74, 
pp6, 23. 

Combination  bridges,  §80,  pp3,  6,  35. 
bridges,  Design  of,  §80,  pp6,  35. 
bridges,  Design  of  pins  for,  §80,  p38. 
bridges,  General  forms  of,  §80,  p35. 
bridges,  Hip  joint  in,  §80,  p38. 
bridges,  Joints  for,  §80,  pp35,  37. 
bridges,  Use  of  steel  in,  §80,  p6. 
bridges,  Use  of  wrought-iron  in,  §80,  p6. 
roof  trusses,  Chord  joints  for,  §81,  p48. 
Combined  stresses,  Specifications  relating  to, 
§74,  ppll,  30. 

Common  rafter,  Definition  of,  §81,  p6. 
Compression  members,  Specifications  relating 
to  design  of,  §74,  pplO,  12,  29,  35. 
verticals  of  rtb,  Design  of,  §79,  p31. 
Compressive  working  stresses  for  timber,  §80, 
p5. 

Concentrated  loads,  Systems  of,  §74,  p61 . 
Concrete,  Use  of,  for  piers  and  abutments, 
§82,  p63. 

Connection  angles  for  floor,  Specifications 
for,  §74,  ppl4,  35. 

Bottom  lateral,  for  rtb,  §79,  p60. 
of  bracket  to  floorbeam,  Drawing  of,  §83, 
p24. 

of  intermediate  floorbeams.  of  rtb  to  truss, 
§79,  P15. 

of  members  to  each  other  in  rtb,  §79, 
p51. 

of  stringer  to  floorbeam  in  rtb,  §79,  p9. 
of  web  members  to  chords  in  Towne  lattice 
truss,  §80,  p32. 

Connections,  Field,  Specifications  relating  to, 
§74,  p47. 

Floor,  for  hb,  Design  of,  §78,  pi. 

Floor,  Specifications  relating  to,  §74, 
ppl3,  34. 

for  roof  trusses,  §81,  p44. 

Lateral,  for  hb,  Design  of,  §78,  p43. 
Construction  of  abutments,  §82,  p62. 
of  bridges,  Specifications  for,  §74,  p42. 
of  piers,  §82.  p62. 


Contractor,  Use  of  the  term,  in  bridge  speci¬ 
fications,  §74,  p3. 

Contractors,  Duties  of,  relating  to  laws  and 
ordinances,  §74,  p53. 

Conventional  signs  for  rivets,  §83,  p7. 

Coping  course,  Definition  of,  §82,  p2. 

Cost  of  bridge  work,  §82,  pp6,  7,  9. 

Counters  of  riveted  trusses,  Specifications  for, 
§74,  PP18,  38. 
of  rtb,  Design  of,  §79,  p30. 

Course,  Belt,  of  a  pier,  §82,  p23. 

Bridge-seat,  Definition  of,  §82,  p2. 
Bridge-seat,  Design  of,  §82,  p65. 

Coping,  of  a  pier,  Definition  of,  §82,  p2. 
Top,  of  a  pier,  Definition  of,  §82,  p2. 
Crimped  stiffeners,  §75,  p32. 

Crossing,  Bridge,  Direction  of,  §82,  p4. 

Bridge,  Skew,  §82,  p4. 

Crushing  of  piers,  §82,  p25. 

Current,  Pressure  of,  on  piers,  §82,  p28. 
Curve  of  flange  areas,  §75,  pp7,  17. 
Curved-wing  abutment,  Definition  of,  §82, 
p56. 

-wing  abutments,  Design  of,  §82,  p58. 
Cutwaters  for  piers,  Forms  of,  §82,  p20. 

for  piers,  Object  of,  §82,  p3. 

Cylinders,  Metallic,  Use  of,  for  piers,  §82,  p64. 

D 

Data,  Bridge,  General  form  of,  §74,  p55. 
for  a  100-foot-span  roof  truss,  §81,  p21. 
for  a  rtb,  §79,  pi. 

for  a  60-foot-span  roof  truss,  §81,  pl4. 
for  an  8-foot-span  roof  truss,  §81,  p30. 
for  an  I-beam  hb,  §76,  ppl,  4. 
for  an  I-beam  railroad  bridge,  §76,  pl2. 
for  bridges,  Specifications  relating  to,  §74, 
pplO,  29. 
for  hb,  §77,  pi. 

for  plate-girder  railroad  bridge,  §76,  pl9. 
Dead-load  moments  in  intermediate  floor- 
beams  of  rtb,  §79,  pll. 

-load  moments  in  rtb,  §79,  p23. 

-load  moments  in  stringers  of  rtb,  §79,  p5. 
load  on  end  floorbeam  of  hb,  §77,  p22. 
load  on  I-beam  hb,  §76,  p7. 
load  on  I-beam  railroad  bridge,  §76,  pl5. 
load  on  intermediate  floorbeams  of  hb,  §77, 
pl3. 

load  on  plate-girder  railroad  bridge,  §76, 

p22. 

load  on  railroad  bridges,  Specifications  for, 
§74,  pp7,  24. 

load  on  roof  trusses,  §81,  p8. 

-load  shears  in  intermediate  floorbeams  of 
rtb,  §79,  pll. 

-load  shears  in  rtb,  §79,  p23. 


X 


INDEX 


Dead — (Continued) 

-load  shears  in  stringers  of  rtb,  §79,  p5. 
-load  stresses  in  hb,  §77,  p29. 

-load  stresses  in  roof  trusses,  §81,  ppl6, 
23,  33. 

loads  assumed  in  bridge  design,  §74,  p66. 
Deck  bridges,  Specifications  for  flooring  of, 
§74,  P14. 

girders,  Specifications  as  to  spacing  of, 
§74,  pp5,  23. 

plate-girder  bridges,  §75,  pl7. 

Depth  of  bridge,  Specifications  relating  to, 
§74,  pp5,  23. 

of  I-beam  railroad  bridge,  §76,  pl6. 
of  I  beams  for  hb,  §76,  p3. 
of  I  beams  for  railroad  bridge,  §76,  pl4. 
of  intermediate  floorbeams  for  rtb,  §79,  plO. 
of  plate  girders  for  railroad  bridge,  §76, 

p21. 

of  roof  truss,  Definition  of,  §81,  p5. 
of  stringers  for  rtb,  §79,  p3. 

Design  of  a  plate-girder  railroad  bridge,  §76, 
pl9. 

of  a  rtb,  §79,  pi. 
of  abutments,  §82,  p48. 
of  an  I-beam  hb,  §76,  pi. 
of  bearings  for  hb,  §78,  p40. 
of  bearings  for  rtb,  §79,  p61. 
of  chord  splices  for  rtb,  §79,  p48. 
of  combination  bridges,  §80,  pp6,  35. 
of  end  floorbeam  for  hb,  §77,  p22.  ■ 
of  end  struts  for  rtb,  §79,  pl8. 
of  flanges  for  plate-girder  railroad  bridge, 
§76,  p31. 

of  floor  system  for  hb,  §77,  p4. 
of  floor  system  for  rtb,  §79,  p3. 
of  hb,  §77,  pi. 

of  I-beam  railroad  bridge,  §76,  pl2. 
of  I  beams,  §75,  p2. 

of  intermediate  floorbeams  for  hb,  §77,  pl3. 
of  intermediate  floorbeams  of  rtb,  §79,  plO. 
of  ioints  of  rtb,  §79,  p51. 
of  lateral  connections  for  hb,  §78,  p43. 
of  lateral  system  of  hb,  §77,  p42. 
of  lateral  system  of  rtb,  §79,  p38. 
of  main  members  of  hb,  §77,  p26. 
of  main  members  of  rtb,  §79,  p27. 
of  piers,  §82,  plO. 

of  pins  for  combination  bridges,  §80,  p38. 
of  pins  for  hb,  §78,  pl6. 
of  plate-girder  flanges,  §75,  p5. 
of  plate-girder  web,  §75,  plO. 
of  plate  girders,  General  features  of,  §75, 
pl7. 

of  roof  trusses,  §81,  p41. 

of  sidewalk  brackets  for  hb,  §77,  pp20,  25. 

of  stringers  for  rtb,  §79,  p3. 


Design — (Continued) 
of  trusses  for  rtb,  §79,  p21. 
of  web  splices  for  plate  girders,  §75,  p20. 
Detail  drawings  for  I-beam  hb,  §76,  pll. 
Details,  Bridge,  Specifications  relating  to, 
§74,  ppll,  30. 

of  hb  (Plates),  §83,  ppll,  19,  25,  31. 
of  I-beam  railroad  bridge,  §76,  pl7. 
Diagonals  of  hb,  Design  of,  §77,  p35. 

of  rtb,  Design  of,  §79,  p30. 

Diagram,  Clearance,  for  bridge,  §74,  p57. 
Diaphragms  for  I-beam  hb,  §76,  pll. 
Dimension  lines,  Location  of,  in  drawings, 
§83,  p2. 

Over-all,  Definition  of,  §83,  p3. 

Dimensions,  Specifications  relating  to  varia¬ 
tions  in,  §74,  p46. 

Distance  between  roof  trusses,  §81,  p4. 
Divergence  of  chord  members  in  hb,  §78, 
p30. 

Douglass  fir,  Working  stresses  in,  §80,  p4. 
Drawing  of  bridge  joints,  §83,  pp20,  28. 
of  bridge  members,  §83,  pplO,  19. 
of  bridge  verticals,  §83,  pp20,  27. 
of  eyebars,  §83,  p21. 
of  lateral  system,  §83,  p31. 
of  pin  plates,  §83,  p25. 
plates,  General  directions  for  making,  §83, 

p8. 

plates  of  hb  details,  §83,  ppll,  19,  25,  31. 
plates,  Size  of,  §83,  p9. 

Skeleton,  of  a  truss,  §83,  plO. 

Drawings,  Bridge,  Size  of,  §83,  p8. 

Location  of  dimensions  on,  §83,  p2. 
Numbering  of,  §83,  p8. 

Use  of  center  lines  in,  §83,  pi. 

Use  of  shortened  views  in,  §83,  p3. 
Working,  submitted  by  contractor,  §74,  p4. 
Drift  Effect  of,  on  piers,  §82,  p29. 

Drilling,  Specifications  relating  to,  §74,  p47. 

E 

Eccentricity  of  bottom  chord  of  rtb,  §79,  p29. 

of  top  chord  of  rtb,  §79,  p37. 

Employment  of  men,  Specifications  relating 
to,  §74,  p53. 

End  floorbeam  for  hb,  Design  of,  §77,  p22. 
frames  for  rtb,  Design  of,  §79,  pl8. 
post  of  hb,  Connection  of,  to  portal,  §78, 
p45. 

post  of  hb,  Effect  of  wind  on,  §77,  p51. 
post  of  rtb,  Design  of,  §79,  pp37,  46. 
stiffeners  for  plate  girders,  §75,  p31. 
struts  for  rtb,  Design  of,  §79,  pl8. 

Engineer,  Use  of  the  term,  in  bridge  specifica¬ 
tions,  §74,  p3. 

Equipment  of  bridges,  Maximum,  §74  p57. 


INDEX 


xi 


Erection  of  bridges,  Specifications  relating  to, 
§74,  p52. 

Estimates,  Preliminary,  for  bridge  construc¬ 
tion,  §82,  pp6,  7,  9. 

Expansion  of  bridges,  Specifications  relating 
to,  §74,  ppl3,  32. 

rpllers  for  bridges,  Specifications  for,  §74, 
pp20,  40, 50. 
rollers  for  hb,  §78,  p42. 
rollers  for  rtb,  §79,  p62. 

Extension  of  time  in  bridge  contracts,  §74, 
p4. 

Extra  work,  Specifications  relating  to,  §74, 
p53. 

Eyebar  heads.  Drawing  of,  §83,  p7. 
tests,  Specifications  for,  §74,  p45. 

Eye  bars,  Drawing  of,  §83,  p21. 

Minimum  thickness  of,  §74,  pl8. 
Specifications  relating  to,  §74,  p49. 


Failure  of  piers,  Causes  of,  §82,  p24. 

Fascia  girder.  Definition  of,  §77,  p5. 

girders  of  hb,  Connection  of,  to  bracket, 

§78,  p3. 

Fence  for  hb,  Connection  of,  to  bracket,  §78, 

p3. 

Field  connections,  Specifications  relating  to, 

§74,  p47. 

riveting  of  splices,  Specifications  relating 
to. .§74,  p52. 

Fillers,  Loose,  for  plate  girders,  §75,p33. 
Tight,  for  plate  girders,  §75,  p33. 

Final  test  of  a  bridge,  Specifications  relating 
to,  §74,  p53. 

Fir,  Douglass,  Working  stresses  in,  §80,  p4. 

Flange  angle  splices,  §75,  p23. 
area,  Calculation  of,  §75,  p6. 
areas,  Curve  of,  §75,  pp7,  19. 
members  for  plate  girders,  Length  of,  §75, 
p7. 

members,  Specifications  relating  to,  §74, 

P48. 

-plate  splices,  §75,  p26. 
plates  for  plate-girder  railroad  bridge, 
Lengths  of,  §76,  p36. 

plates  for  plate  girders,  Length  of,  §75,  p27. 
plates  in  intermediate  floorbeams  of  rtb, 
Length  of,  §79,  pl3. 

plates,  Vertical,  Plate  girders  with,  §75,  pl8. 
plates,  Vertical,  Splices  in,  §75,  p28. 
rivets  for  plate  girders,  Pitch  of,  §75,  pl4. 
rivets  in  floorbeams  of  hb,  §77,  ppl9,  25. 
rivets  in  intermediate  floorbeams  of  rtb, 
§79,  pl4. 

rivets  in  plate-girder  railroad  bridge,  Pitch 
of,  §76,  p29. 


Flange — (Continued) 

rivets  in  plate  girders,  Specifications  for, 
§74,  ppl5,  36. 

rivets  in  stringers  of  rtb,  §79,  p7. 
splices  for  plate  girders,  Specifications  for, 
§74,  ppl6,  37. 

Flanges,  Floorbeam,  for  hb,  Design  of,  §77, 
ppl9,  24. 

for  plate-girder  railroad  bridge,  Design  of, 
§76,  P31. 

Inclined,  Plate  girders  with,  §75,  pl7. 
of  intermediate  floorbeams  of  rtb,  Design 
of,  §79,  P12. 

of  plate  girders,  Design  of,  §75,  p5. 
of  plate  girders,  Specifications  for,  §74, 
ppl6,  36. 

of  stringers  of  rtb,  Design  of,  §79,  p6. 

Flaring-wing  abutment,  Definition  of,  §82, 
p53. 

-wing  abutments,  Design  of,  §82,  p57. 

Floor  connections  for  hb,  Design  of  §78,  pi. 
connections,  Specifications  relating  to,  §74, 
ppl3,  34. 

for  hb,  Details  of,  §78,  pi. 
for  I-beam  hb,  §76,  plO. 
members,  Specifications  for  design  of,  §74, 
pplO,  13,  32. 

system  for  hb,  Design  of,  §77,  p4. 
system  for  rtb,  Design  of,  §79,  p3 
system  of  a  bridge,  General  methods  of 
arranging,  §74,  p58. 

systems,  Specifications  relating  to  details 
of,  §74,  PP13,  32. 

Floorbeam  connections,  Specifications  for, 
§74,  ppl3,  34. 

End,  for  hb,  Design  of,  §77,  p22. 

End,  of  hb,  Connection  of ,  to  truss,  §78,  pl2 
flanges  for  hb,  Design  of,  §77,  ppl9,  24. 
gussets,  §79,  pl7. 

Intermediate,  Drawing  of,  §83,  p22. 
of  hb,  Connection  of,  to  truss,  §78,  p9. 
of  rtb,  Connection  of,  to  stringer,  §79,  p9. 
web  for  hb,  Design  of,  §77,  ppl8,  24. 

Floorbeams,  End,  Specifications  for,  §74, 
pl4. 

for  Towne  lattice  truss,  §80,  p32. 
Intermediate,  for  hb,  Design  of,  §77,  pl3. 
Intermediate,  for  rtb,  Design  of,  §79,  plO 
Intermediate,  of  rtb,  Connection  of,  to 
truss,  §79,  pl5. 

of  hb,  Connection  of,  to  roadway  stringers, 
§78,  p5. 

of  hb,  Connection  of,  to  sidewalk  bracket, 
§78,  pll. 

Floors,  Paved,  Specifications  for,  §74,  p34. 
Solid,  Specifications  for,  §74,  pl4. 

Wooden,  Specifications  for,  §74,  p32. 


135—39 


INDEX 


Xll 


Footings,  Abutment,  Design  of,  §82,  p52. 
for  piers,  General  remarks  on,  §82,  pl3. 
of  a  pier,  §82,  p3. 

Foundation  of  a  pier,  Failure  of,  §82,  p26. 
of  a  pier,  Pressure  on,  §82,  p43. 

Frame,  Transverse,  of  lib,  Connection  of,  to 
truss,  §78,  p43. 

Frames,  End,  for  rtb,  Design  of,  §79,  pl8. 
for  I-beam  hb,  §76,  pll. 

Transverse,  for  hb,  Design  of,  §77,  p45. 
Transverse,  for  rtb,  Arrangement  of,  §79, 
p41. 

Frost  batter  of  a  parapet,  §82,  p50. 

G 

Girder,  Fascia,  Definition  of,  §77,  p5. 

Girders,  Fascia,  for  hb,  Connection  of,  to 
bracket,  §78,  p3. 

Plate  (see  Plate  girders). 

Grip  of  rivets,  Specifications  for,  §74,  pl2. 

Guard  timbers  for  bridges,  Specifications  for, 
§74,  PP13,  32. 

Gussets,  Floorbeam,  §79,  pl7. 

II 

Half-through  bridges,  Specifications  relating 
to  use  of,  §74,  p6. 

-through  plate-girder  bridges,  §75,  pl7. 

Hand  railing  for  highway  bridges.  Specifica¬ 
tions  for,  §74,  p35. 

Head  of  a  T  abutment,  Definition  of,  §82, 
p48. 

Heads,  Eyebar,  Drawing  of,  §83,  p7. 

Heel  joints  for  steel  roof  trusses,  §81,  p51. 
joints  for  wooden  roof  trusses,  §81,  p47. 

Height  of  a  bridge,  Clear,  §74,  p57. 
of  piers,  Conditions  affecting,  §82,  pl4. 

Highway  bridge,  Bridge-seat  plan  for,  §78, 
p45. 

bridge,  Design  of,  §77,  pi. 
bridge,  Design  of  bearings  for,  §78,  p40. 
bridge,  Design  of  floor  connections  for,  §78, 
pi. 

bridge,  Design  of  floor  system  for,  §77,  p4. 
bridge,  Design  of  lateral  connections  for, 
§78,  p44. 

bridge,  Design  of  lateral  system  of,  §77,  p42. 
bridge,  Design  of  main  members  for  §77, 

p26. 

bridge,  Design  of  pins  and  pin  plates  for, 
§78,  P16. 

-bridge  details  (Plates),  §83,  ppll,  19,  25, 
31. 

bridge,  I-beam,  Design  of,  §76,  pi. 
bridge,  Kinds  of,  §77,  p2. 
bridge,  Loads  on,  §77,  pp26,  29,  31. 
bridge,  Longitudinal  thrust  in,  §77,  p32. 


Highway — (Continued) 

bridge,  Stresses  in  main  members  of,  §77, 

p26. 

bridge,  Weight  of,  §77,  p30. 
bridge,  Width  of,  §77,  p3. 
bridges,  Live  loads  used  for,  §74,  p62. 
bridges,  Weights  of,  §74,  p66. 

Highways,  Piers  in,  §82,  pl4. 

Hip  joint  in  combination  bridges,  §80,  p38. 
vertical,  Drawing  of,  §83,  p27. 
vertical  of  hb,  Design  of,  §77,  p37. 
vertical  of  rtb,  Design  of,  §79,  p33. 

Holes,  Rivet,  Specifications  relating  to.  §74, 
p47. 

Howe  truss,  Wooden,  Description  of,  §80,  p24. 
truss,  Wooden,  Lateral  system  for,  §80,p31. 
truss,  Wooden,  Splices  for,  §80,  p28. 

I 

I-beam  railroad  bridge,  Depth  of,  §76,  pl6. 
-beam  railroad  bridge,  Design  of,  §76,  pl2. 
-beam  railroad  bridge  Details  of,  §76,  pl7. 
-beam  railroad  bridge,  Plan  of,  §76,  pl7. 
beams,  Design  of,  §75,  p2. 
beams  for  hb,  Arrangement  of,  §76,  p23. 
beams  for  hb,  Depth  of,  §76,  p3. 
beams  of  hb,  Spacing  of,  §76,  p3. 
beams  for  railroad  bridge,  Depth  of,  §76, 
pl4. 

beams  for  railroad  bridge,  Spacing  of,  §76, 
pl4. 

beams,  Specifications  relating  to  connec¬ 
tions  of,  §74,  pl3. 

Ice  breakers  for  piers,  Object  of,  §82,  p3. 
Effects  of,  on  piers,  §82,  p29. 

Pressure  of,  on  piers,  §82,  p29. 

Impact  and  vibration,  Allowance  for.  in  hb, 
§77,  pp27,  29. 

and  vibration,  Allowance  for,  in  I-beam 
railroad  bridge,  §76,  pl4. 
and  vibration,  Allowance  for,  in  interme¬ 
diate  floorbeams  of  rtb,  §79,  plO. 
and  vibration.  Allowance  for,  in  rtb,  §79, 

p22. 

and  vibration,  Allowance  for,  in  stringers 
of  rtb,  §79,  p4. 

and  vibration,  Specifications  relating  to, 
§74,  pp7,  26. 

Effect  of,  on  bridge  stresses,  §74,  p63. 
Inclined  flanges,  Plate  girders  with,  §75,  pl7. 
Inspection  of  bridges,  Specifications  relating 
to,  §74,  p53. 

Inspectors,  Specifications  relating  to,  §74,  p53. 
Intermediate  floorbeam,  Drawing  of,  §83, 

p22. 

floorbeams  tor  hb,  Design  of,  §77.  pl3. 
floorbeams  for  rtb,  Design  of.  §79,  plO. 


INDEX 


Xlll 


Intermediate — (Continued) 

floorbeams  of  rtb,  Connection  of.  to  truss, 
§15,  97. 

Invitation,  Letter  of,  §74,  pp3,  54. 

Iron,  Wrought,  Specifications  for,  §74,  p43. 

J 

Joint,  Peak,  for  steel  roof  truss,  §81,  p50. 

Peak,  for  wooden  roof  truss,  §81,  p44. 
Joints,  Bridge,  Drawing  of,  §83,  pp20,  28. 
Chord,  for  combination  roof  trusses,  §81, 
p48. 

Chord,  for  steel  roof  trusses,  §81,  p53. 
Chord,  for  wooden  roof  trusses,  §81,  p46. 
for  combination  bridges,  §80,  pp35,  37. 
for  steel  roof  trusses,  §81,  p49. 
for  wooden  roof  trusses,  §81,  p44. 

Heel,  for  steel  roof  trusses,  §81,  p51. 

Heel,  for  wooden  roof  trusses,  §81,  p47. 
in  riveted  trusses.  §79,  p51. 
in  stone  masonry,  §82,  p64. 
of  rtb,  Design  of,  §79,  p51. 

Rafter,  for  steel  roof  trusses,  §81,  p49. 
Rafter,  for  wooden  roof  trusses,  §81,  p44. 

K 

Kingpost,  Definition  of,  §80,  p7. 
truss,  Description  of,  §80,  p7. 
truss,  Stresses  in,  §80,  p9. 
truss,  Uses  of,  §80,  p7. 

Kingrod  bridge,  Example  of,  §80,  pl2. 
truss,  Description  of,  §80,  p8. 
truss,  Stresses  in,  §80,  p9. 

Knee  bracing  of  bridges,  Specifications  for, 
§74  pp22,  41 

Li 

Lateral  bracing  between  stringers  of  rtb,  §79, 

p6. 

bracing  for  bridges,  Specifications  for,  §74, 
pp21,  41. 

connections  for  hb,  Design  of,  §78,  p43 
system,  Drawing  of,  §83,  p31. 
system  for  hb,  Design  of,  §77,  p42. 
system  for  plate-girder  railroad  bridge,  §76, 
p43. 

system  for  Towne  lattice  truss,  §80,  p35, 
system  for  wooden  Howe  truss,  §80,  p31. 
system  of  rtb,  Design  of,  §79,  p38. 
system  of  rtb,  Stresses  in,  §79,  p38. 
systems  of  roof  trusses,  §81,  p42. 

Laterals,  Lower,  Connection  of,  to  truss  in 
rtb,  §79,  p60. 

Lattice  bars,  Specifications  for,  §74,  ppl2,  31. 

truss,  Towne,  Description  of,  §80,  p32. 
Laws,  Duties  of  contractor  relating  to,  §74, 
p53. 


Length  of  flange  plates  in  intermediate  floor- 
beams  of  rtb,  §79,  pl3. 
of  intermediate  floorbeams  for  rtb,  §79,  plO. 
Over- all,  Definition  of,  §83,  p3. 

Panel,  of  roof  truss,  §81,  p6. 

Lengths  of  plate-girder  members,  §75,  pl9. 
Panel,  Specifications  relating  to,  §74, 
pp5,  23. 

Letter  of  invitation,  §74,  pp3,  54. 

Line,  Neat,  Definition  of,  §82,  p2. 

Lines,  Dimension,  Location  of,  in  drawings, 
§83,  p2. 

Working,  of  I-beam  railroad  bridge,  §76, 
pl8. 

Live-load  moments  in  intermediate  floor- 
beams  of  rtb,  §79,  plO. 

-load  moments  in  rtb,  §79,  p21. 
load  on  bridges,  Specifications  for,  §74, 
pp7,  24. 

load  on  end  floorbeam  of  hb,  §77,  p24. 
load  on  I-beam  hb,  §76,  p6. 
load  on  I-beam  railroad  bridge,  §76,  pl4. 
load  on  intermediate  floorbeams  of  hb,  §77, 
pl5. 

load  on  plate-girder  railroad  bridge,  §76, 
p23. 

-load  shears  in  intermediate  floorbeams  of 
rtb,  §79,  plO. 

-load  shears  in  rtb,  §79,  p21. 

-load  stresses  in  hb,  §77,  p26. 
loads  for  highway  bridges,  §74,  p62. 
loads  used  for  railroad  bridges,  §74,  p61. 

Load,  Dead,  on  bridges,  Specifications  for, 
§74,  pp7,  24. 

Dead,  on  end  floorbeam  of  hb,  §77,  p22. 
Dead,  on  hb,  §77,  p29. 

Dead,  on  I-beam  hb,  §76,  p7. 

Dead,  on  I-beam  railroad  bridge,  §76,  pl5. 
Dead,  on  intermediate  floorbeams  of  hb, 
§77,  P13. 

Dead,  on  plate-girder  railroad  bridge,  §76, 

p22. 

Dead,  on  roof  trusses,  §81,  p8. 

Live,  on  bridges,  Specifications  for,  §74, 
PP7,  24. 

Live,  on  end  floorbeam  of  hb,  §77,  p24. 
Live,  on  hb,  §77,  p26. 

Live,  on  I-beam  hb,  §76,  p6. 

Live,  on  I-beam  railroad  bridge,  §76,  pl4. 
Live,  on  intermediate  floorbeams  of  hb,  §77, 
pl5. 

Live,  on  plate-girder  railroad  bridge,  §76, 
p23. 

Snow,  on  roof  trusses,  §81,  p8. 

Wind,  Allowance  for,  in  stringers  of  rtb, 
§79,  P5. 

Wind,  on  hb,  §77,  p31. 


XIV 


INDEX 


Load — (Continued) 

Wind,  on  I-beam  railroad  bridge,  §76,  pl5. 
Wind,  on  plate-girder  railroad  bridge,  §76, 
p25. 

Loading  of  bridges,  Specifications  relating  to, 
§74,  pp7,  24. 

Systems  of,  used  for  railroad  bridges,  §74, 

p61. 

Loads,  Dead,  Assumed  in  bridge  design,  §74, 

p66. 

Live,  used  for  highway  bridges,  §74,  p62. 
Live,  used  for  railroad  bridges,  §74,  p61. 
on  roof  trusses,  §81,  p8. 

Panel,  on  roof  trusses,  §81,  p9. 

Location  of  bridges,  §74,  p56. 

of  piers  and  abutments,  §82,  p4. 
Longitudinal  force  on  bridges,  Specifications 
for,  §74,  pp8,  27. 
shear  in  a  beam,  §75,  pplO,  12. 
thrust,  Allowance  for,  in  rtb,  §79,  p25. 
thrust,  Effect  of,  on  piers,  §82,  p31. 
thrust  in  hb,  §77,  p32. 

Loose  fillers  for  plate  girders,  §75,  p33. 

Lower  lateral  truss  of  hb,  Design  of,  §77, 
pp44,  49. 

lateral  truss  of  rtb,  Design  of,  §79,  p45. 
lateral  truss  of  rtb,  Stresses  in,  §79,  p39. 

M 

Main  bridge  seat,  Definition  of,  §82,  p3. 

rafter,  Definition  of,  §81 ,  p5. 

Masonry,  Stone,  joints  in,  §82,  p64. 

Materials  for  bridges,  Specifications  for,  §74, 
p42. 

for  piers  and  abutments,  §82,  p62. 
for  roof- truss  covering,  §81,  p7. 
for  roof  trusses,  §81,  p41. 

Maximum  bending  moment  in  I-beam  railroad 
bridge,  §76,  ppl4,  15. 
equipment  of  bridges,  §74,  p57. 
moments  in  rtb,  §79,  p25. 
shears  in  rtb,  §79,  p25. 

Members,  Bridge,  Drawing  of,  §83,  pl9 
Main,  of  hb,  Design  of,  §77,  p26. 

Main,  of  hb,  Stresses  in,  §77,  p26. 

Main,  of  rtb,  Design  of,  §79  p27. 

Main,  of  rtb,  Stresses  in,  §79,  p26. 

Web,  of  hb,  Design  of,  §77,  p35. 

Web,  of  rtb.  Design  of,  §79,  p30. 

Men,  Specifications  relating  to  employment  of, 
§74,  p53. 

Mill  orders,  Specifications  relating  to,  §74,  p54. 

tests,  Specifications  relating  to,  §74,  p44. 
Minimum  thickness  of  bridge  parts,  §74,  p30. 
thickness  of  material,  Specifications  for, 
§74,  ppll,  30. 

Modulus,  Section,  of  plate  girder  §75,  p3. 


Moment,  Bending,  of  pins  of  hb,  §78,  pl6. 
Dead-load,  in  intermediate  floorbeams  of 
rtb,  §79,  pll. 

of  water  pressure  on  piers,  §82,  p35. 
Resisting,  of  plate-girder  web,  §75,  p20. 
Resisting,  of  web-splice  rivets,  §75,  p21. 
Moments,  Dead-load,  in  rtb,  §79,  p23. 
Dead-load,  in  stringers  of  rtb,  §79,  p5. 
from  wind  pressure  on  piers,  §82,  p33. 
in  end  floorbeam  of  hb,  §77,  pp22,  24 
in  intermediate  floorbeams  of  hb,  §77,  ppl5, 
18. 

Live-load,  in  intermediate  floorbeams  of 
rtb,  §79,  plO. 

Live-load,  in  rtb,  §79,  p21. 

Live-load,  in  stringers  of  rtb,  §79,  p3. 
Maximum,  in  rtb,  §79,  p25. 

Resisting,  of  piers.  §82,  p36. 

Monitor,  Stresses  in  roof  truss  with,  §81,  p30. 
Monitors  on  roof  trusses,  §81,  p4. 

N 

Name  plate  for  a  bridge,  Specifications  rela¬ 
ting  to,  §74,  p53. 

Neat  line  of  a  pier,  Definition  of,  §82,  p2. 
Nest,  Roller,  for  hb,  §78,  p42. 

Nosings  for  piers,  Forms  of,  §82,  p20. 

of  piers,  Object  of,  §82,  p3. 

Notation  for  bridge  drawings,  §83,  p8. 
Numbering  of  drawings,  §83,  p8. 

Nuts,  Pin,  Drawing  of,  §83,  p7. 

Pin,  Specifications  relating  to,  §74,  p50. 

O 

Oak,  White,  Working  stresses  in,  §80,  p4. 

Old  structures,  Specifications  relating  to  re¬ 
placement  of,  §74,  p52. 

Orders,  Mill,  Specifications  relating  to,  §74, 
p54. 

Over-all  dimension.  Definition  of,  §83,  p3. 

-all,  Length,  Definition  of,  §83,  p3. 
Overturning  of  piers,  Calculations  for,  §82, 
p33. 

of  piers,  Forces  tending  to  cause,  §82,  p24. 
Resistance  of  piers  against,  §82,  p36 

P 

Packing  of  bottom  chord  of  hb,  §78,  p29. 
Painting  of  bridges,  Specifications  for,  §74, 
p51. 

Panel  length  of  roof  truss,  §81,  p6. 

lengths,  Specifications  relating  to,  §74, 
PP5,  23. 

loads  on  roof  trusses,  §81,  p9. 

Parapet  of  a  bridge  pier,  Definition  of,  §82- 
p3. 

of  an  abutment,  Dimensions  of,  §82,  p50. 


INDEX 


xv 


Parapets,  Construction  of,  §82,  p65. 

Patent  devices,  Responsibility  of  contractor 
for  the  use  of,  §74,  p4. 

Paved  floors  for  bridges,  Specifications  for, 
§74,  p34. 

Peak  joint  for  steel  roof  truss,  §81,  p50. 

joint  for  wooden  roof  truss,  §81,  p44. 
Pedestal  blocks  for  abutments,  §82,  p51. 
blocks  for  piers,  §82,  pp3,  12. 
for  hb,  Design  of,  §78,  p40. 
pier,  Definition  of,  §82,  p2. 

Pedestals  for  high  trestles,  §82,  pl7. 
for  rtb.  Design  of,  §79,  p62. 
for  trestles,  Construction  of,  §82,  p66. 
for  trusses,  Specifications  for,  §74,  pp20,  40. 
Pier  abutment,  Definition  of,  §82,  p2. 
abutments,  Uses  of,  §82,  p61, 
calculations,  §82,  p31. 
construction,  §82,  p62. 

Definition  of,  §82,  pi 
design,  §82,  plO. 
location,  §82,  p4. 

Pedestal,  Definition  of,  §82,  p2. 
wings,  Definition  of,  §82,  p2. 

Piers,  Batter  of,  §82,  pl2. 

Calculations  for  overturning  of,  §82,  p33. 
Centrifugal  force  on,  §82,  p30. 

Conditions  affecting  dimensions  of,  §82,  plO. 
Conditions  affecting  height  of,  §82,  pl4. 
Crushing  of,  §82,  p25. 

Economic  arrangement  of,  §82,  p5. 

Effect  of  draft  on,  §82,  p29. 

Effect  of  ice  on,  §82,  p29. 

Effect  of  longitudinal  thrust  on,  §82,  p31. 
Estimates  for,  §82,  p6. 

Failure  of,  from  imperfect  foundation,  §82, 

p26. 

Footings  for,  General  remarks  on,  §82,  pl3. 
for  running  streams,  §82,  p20. 
for  trestles,  §82,  pl6. 
for  trestles,  Construction  of,  §82,  p66. 
Forces  tending  to  cause  sliding  of,  §82,  p25. 
Forces  tending  to  overturn,  §82,  p24. 
Forms  of  cutwaters  for,  §82,  p20. 
in  streets,  §82,  pl4. 

Materials  used  for,  §82,  p62. 

Moment  of  water  pressure  on,  §82,  p35. 
Moments  of  wind  pressure  on,  §82,  p33. 
near  railroad  tracks,  §82,  pl6. 

Number  of,  §82,  p7. 

Plans  for,  §82,  p9. 

Pressure  of  ice  on,  §82,  p29. 

Pressure  of  water  on,  §82,  p28. 

Pressure  on  foundation  of,  §82,  p43. 
Pressure  on  subfoundation  of,  §82,  p43. 
Resistance  of,  to  overturning,  §82,  p36. 
Resistance  of,  to  sliding,  §82,  p41. 


Piers — (Continued) 

Resisting  moments  of,  §82,  p36. 
Specifications  for,  §82,  p64. 

Stability  of,  §82,  pp23,  26. 

Undermining  of,  §82,  p66. 

Use  of  metallic  cylinders  for,  §82,  p64. 
Wind  pressure  on,  §82,  p27. 

Pin-connected  trusses,  Specifications  for  de¬ 
tails  of,  §74,  ppl8,  38. 

Pinholes,  Specifications  relating  to,  §74,  p49. 
Pin  nuts,  Drawing  of,  §83,  p7. 

nuts,  Specifications  relating  to,  §74,  p50. 
plates,  Drawing  of,  §83,  p25. 
plates  for  hb,  Design  of,  §78.  pl6. 
plates,  Specifications  for,  §74,  ppl9,  39. 
Pine,  White,  Working  stresses  in,  §80,  p4. 

Yellow,  Working  stresses  in,  §80,  p4. 

Pins  for  combination  bridges,  Design  of,  §80, 
p38. 

for  hb,  Design  of,  §78,  pi 6. 

Specifications  for  size  of,  §74,  ppl8,  38. 
Specifications  relating  to,  §74,  p50. 

Pitch  of  flange  rivets  in  plate-girder  railroad 
bridge,  §76,  p29. 

of  roof  truss,  Definition  of,  §81,  p7. 

Plan,  Bridge-seat,  for  hb,  §78,  p45. 
Bridge-seat,  for  rtb,  §79,  p64. 

Definition  of,  as  applied  to  drawings,  §76, 
p3. 

of  I-beam  hb,  §76,  pll. 
of  I-beam  railroad  bridge,  §76,  pl7. 
of  plate-girder  railroad  bridge,  §76,  pl9. 
Plans  for  piers  and  abutments,  §82,  p9. 
Plate-girder  bridges,  Deck,  §75,  pl7. 

-girder  bridges.  Half-through,  §75,  pl7. 
-girder  flanges,  Design  of,  §75,  p5. 

-girder  members,  Lengths  of,  §75,  pl9. 
-girder  railroad  bridge,  Design  of,  §76,  pl9. 
girder,  Section  modulus  of,  §75,  p3. 

-girder  web,  Shear  in,  §75,  pl2. 

-girder  web,  Stiffeners  for,  §75,  pl3. 
girders,  Bearings  for,  §75,  p30 
girders,  Design  of  splices  for,  §75,  pl9. 
girders,  Design  of  webs  for,  §75,  plO. 
girders,  Distribution  of  reaction  on,  §75, 
p31. 

girders  for  railroad  bridge,  Depth  of,  §76, 

p21. 

girders  for  railroad  bridge,  Spacing  of,  §76, 

p21. 

girders,  General  features  of  design  of,  §75, 
P17. 

girders,  Length  of  flange  members  for,  §75, 
p7. 

girders,  Specifications  for  details  of,  §74, 
ppl4,  35. 

girders  with  inclined  flanges,  §75,  pl7. 


XVI 


INDEX 


Plate — (Continued) 

girders  with  vertical  flange  plates,  §75, 
pl8. 

'Name,  Specifications  relating  to,  §74,  p53. 
Splice,  Definition  of,  §75,  p20. 

Plates,  Drawing,  General  directions  for  ma¬ 
king,  §83,  p8. 

Drawing,  Size  of,  §83,  p9. 

Flange,  for  plate-girder  railroad  bridge,  §76, 
p36. 

Flange,  in  intermediate  floorbeams  of  rtb, 
Length  of,  §79,  pl3. 

Flange,  Specifications  for,  §74,  ppl6,  36. 
of  hb  details,  Description  of,  §83,  ppll,  19, 
25.  31. 

Pin,  Drawing  of,  §83,  p25. 

Pin,  for  hb,  Design  of.  §78,  pl6. 

Pin,  Specifications  for,  §74,  ppl9,  39. 
Reinforcing,  for  plate  girders,  §75,  p31,  33. 
Vertical  flange,  §75,  pl8. 

Web,  Specifications  relating  to,  §74,  p48. 
Pockets  in  bridge  seat  of  abutment,  §82,  p51. 
Portal  bracing,  Specifications  for,  §74,  pp22, 
41. 

for  rtb,  Stresses  in,  §79,  p42. 
of  hb,  Connections  of,  §78,  p45. 
of  hb,  Design  of,  §77,  pp45,  50. 
of  hb,  Stresses  in.  §77,  p45. 
of  rtb,  Design  of,  §79,  p46 
Post,  End  (see  also  End  post). 

End,  of  hb,  Connection  of,  to  portal,  §78, 
p45. 

End,  of  rtb,  Design  of,  §79,  pp87,  46. 
Pressure  of  ice  on  piers,  §82,  p29. 
of  water  on  piers,  §82,  p28, 
of  water  on  piers,  Moment  of,  §82,  p35. 
of  wind  on  bridges,  Specifications  for,  §74, 
pp8,  27. 

on  foundation  of  a  pier,  §82,  p43. 
on  subfoundation  of  a  pier,  §82,  p43. 

Wind,  Allowance  for,  in  intermediate  floor- 
beams  of  rtb,  §79,  pll. 

Wind,  Allowance  for,  in  trusses  of  rtb,  §79, 
p24. 

Wind,  on  piers,  §82,  p27. 

Wind,  on  roof  trusses,  §81,  p9. 

Wind,  on  rtb,  §79,  p38. 

Proposals  for  bridges,  §74,  p3. 

Purlins,  Definition  of,  §81,  p5. 

Q 

Queenpost  truss,  Description  of,  §80,  pl4. 

truss,  Stresses  in,  §80,  pl7. 

Queenrod  bridge  without  diagonals,  §80, 
p23. 

truss.  Description  of,  §80,  pl4. 
truss,  Stresses  in,  §80,  pl7. 


R 

Rafter,  Common,  Definition  of,  §81,  p6. 
Definition  of,  §81,  p5. 
joints  for  steel  roof  trusses,  §81,  p44. 
joints  for  wooden  roof  trusses,  §81,  p44. 
Main,  Definition  of,  §81,  p5. 

Railing,  Hand,  for  highway  bridges,  Specifica¬ 
tions  for,  §74,  p35. 

Railroad  bridge,  I-beam,  Design  of,  §76, 

p2. 

bridges,  Specifications  for  the  design  of,  §74, 
p5. 

bridges,  Weights  of,  §74,  p66. 

tracks,  Piers  near,  §82,  pl6. 

truss  bridge,  Bridge-seat  plan  for,  §79,  p64. 

truss  bridge,  Design  of,  §79,  pi. 

truss  bridge,  Design  of  bearings  for,  §79, 

p61. 

truss  bridge,  Design  of  chord  splices  for,  §79, 
p48. 

truss  bridge,  Design  of  end  struts  for,  §79, 
pl8. 

truss  bridge,  Design  of  intermediate  floor- 
beams  for,  §79,  plO. 

truss  bridge,  Design  of  joints  for,  §79,  p51. 
truss  bridge,  Design  of  lateral  system  of, 
.  §79,  p38. 

truss  bridge,  Design  of  main  members  of, 
§79,  P27. 

truss  bridge,  Design  of  stringers  for,  §79,  p3. 
truss  bridge,  Selection  of  type  of,  §79,  pi. 
truss  bridge,  Stresses  in  main  members  of, 
§79,  p21. 

truss  bridge,  Weight  of,  §79,  p23. 
truss  bridge,  Width  of,  §79,  p3. 

Reaction  on  plate  girders,  Distribution  of,  §/5, 
pp31,  33. 

Reactions  on  roof  trusses,  §81  pll. 

Reaming,  Specifications  relating  to,  §74,  p47. 
Reentrant  angles,  Specifications  relating  to, 
§74,  p46. 

Reinforcing  plates  for  plate  girders,  §75,  p31. 
Rejection  of  materials,  Specifications  relating 
to,  §74,  p45. 

Resisting  moment  of  plate-girder  web,  §75, 

p20 

moment  of  web-splice  rivets,  §75,  p21. 
moments  of  piers,  §82,  p36. 

Reversal  of  stress.  Specifications  relating  to, 
§74,  ppll,  30. 

of  stresses,  Allowance  for,  §74,  p65. 

Rise  of  roof  truss,  Definition  of,  §81,  pp5,  7 . 
Rivet  grip,  Specifications  for,  §74,  pl2. 
heads  on  drawing  plates,  Size  of,  §83,  pll. 
holes,  Specifications  relating  to,  §74,  p47. 
spacing,  Specifications  for,  §74,  ppll,  31. 
steel,  Specifications  for,  §74,  p42. 


INDEX 


xvii 


Riveted  members,  Specifications  relating  to, 
§74,  pp48,  49. 

tension  member  for  pin-connected  trusses, 
Specifications  for,  §74,  ppl8,  39. 
trusses,  Joints  in,  §97,  p51. 
trusses,  Specifications  for,  §74,  ppl7,  37. 
Riveting,  Field,  of  splices,  Specifications  re¬ 
lating  to,  §74,  p52. 

of  girders,  Specifications  relating  to,  §74. 
P17. 

Specifications  relating  to,  §74,  p48. 

Rivets,  Conventional  signs  for,  §83,  p7. 

Flange,  in  intermediate  floorbeams  of  rtb, 
§79,  P14. 

Flange,  in  plate  girders,  Specifications  for, 
§74,  ppl5.  36. 

Flange,  in  stringers  of  jtb,  §79,  p7. 
Flange,  Pitch  of,  in  plate-girder  railroad 
bridge,  §76,  p29. 
in  flange-angle  splices,  §75,  p25. 
in  flanges  of  hb  floorbeams,  §77,  ppl9,  25. 
in  plate  girder  flanges,  Pitch  of,  §75,  pl4. 
Number  of,  in  stiffeners,  §75,  p32. 
Specifications  for  size  of,  §74,  ppll,  31. 
Specifications  relating  to,  §74,  p47. 
Specifications  relating  to  bearing  values  of, 
§74,  ppll, 30. 

Web-splice,  Resisting  moment  of,  §75,  p21. 
Roads,  Piers  in,  §82,  pl4. 

Rocker  bearings  for  plate  girders,  §75,  p34. 
Roller  nest  for  hb,  §78,  p42. 

Rollers,  Expansion,  for  bridges,  Specifications 
for,  §74,  pp20,  40,  50. 
for  hb,  §78,  p42. 
for  rtb,  §79,  p62. 

Roof  truss,  Chord  of,  defined,  §81,  p5. 

-truss  covering,  Materials  for,  §81,  p7. 

truss,  Depth  of,  defined,  §81,  p5. 

truss,  Manner  of  expressing  slope  of,  §81, 

p7. 

truss,  Members  of,  §81,  p5. 
truss,  Panel  length  of,  §81,  p6. 
truss,  Rise  of,  defined,  §81,  pp5,  7. 
truss,  Run  of,  §81,  p7. 
truss,  Span  of,  defined,  §81,  p5. 
truss  with  monitor,  Stresses  in,  §81,  p30. 
trusses,  Connections  for,  §81,  p44. 
trusses,  Dead-load  stresses  in,  §81,  ppl6,  23, 
33. 

trusses,  Design  of,  §81,  p41. 
trusses,  Examples  of  stress  calculations  for, 
§81,  ppl4,  21,  30. 

trusses,  General  methods  of  calculating 
stresses  in,  §81,  pl4. 
trusses,  Lateral  systems  for,  §81,  p42. 
trusses,  Loads  on,  §81,  p8. 
trusses,  Materials  for,  §81,  p41. 


Roof —  (Continued) 

trusses,  Monitors  on,  §81,  p4. 

trusses,  Panel  loads  on,  §81,  p9. 

trusses,  Reactions  on,  §81,  pll. 

trusses,  Snow-load  stresses  in,  §81,  ppl6, 

23,  33. 

trusses,  Types  of,  §81,  pi. 

trusses,  Uses  of,  §81,  pi. 

trusses,  Wind-load  stresses  in,  §81,  ppl8, 

24,  35. 

trusses,  Wind-pressure  on,  §81,  p9. 
trusses,  Working  stresses  for,  §81,  p41. 

Run  of  roof  truss,  Definition  of,  §81,  p7. 

S 

Seat,  Bridge  (see  Bridge  seat). 

Section  modulus  of  plate  girders,  §75,  p3. 
Selection  of  type  of  bridge,  §74,  p56. 

Shapes,  Structural,  Representation  of ,  §83,  p5. 

Structural,  Standard,  §83,  pi. 

Shear  in  plate-girder  web,  §75,  pl2. 

Longitudinal,  §75,  pplO,  12. 

Shearing  stress  in  beams,  Distribution  of,  §75, 
PPlO,  12. 

working  stresses  for  timber,  §80,  p6. 

Shears,  Dead-load,  in  intermediate  floorbeams 
of  rtb,  §79,  pi. 

Dead-load,  in  rtb,  §79,  p23. 

Dead-load,  in  stringers  of  rtb,  §79,  p5. 
in  end  floorbeam  of  hb,  §77,  pp22,  24. 
in  intermediate  floorbeams  of  hb,  §77,  ppl5, 
17. 

Live-load,  in  intermediate  floorbeams  of 
rtb,  §79,  plO. 

Live-load,  in  rtb,  §79,  p21. 

Live  load,  in  stringers  of  rtb,  §79,  p3. 
Maximum,  in  rtb,  §79,  p25. 

Shipment  of  bridge  materials,  Specifications 
for,  §74,  p50. 

Shortened  views  of  bridge  parts,  §83,  p3. 
Sidewalk  bracket,  Drawing  of,  §83,  p22. 
bracket  of  hb,  Connection  of,  to  floorbeam, 
§78,  pll. ' 

bracket  of  hb,  Connection  of,  to  truss,  §78, 
p9. 

brackets  for  hb,  Design  of,  §77,  pp20,  25. 
stringers  for  hb,  Design  of,  §77,  p6. 
stringers  of  hb,  Connection  of,  to  brackets, 
§78,  p3. 

Signs  for  rivets,  §83,  p7. 

Skeleton  drawing  of  a  truss,  §83,  plO. 

Skew  abutment,  Definition  of,  §82,  pp4,  59. 
abutments,  Design  of,  §82,  p59. 
bridge  crossing,  §82,  p4. 

Sliding  of  piers,  Forces  tending  to  cause,  §82, 
p25. 

Resistance  of  piers  to,  §82  p41. 


INDEX 


xviii 


Slope  of  roof  truss,  Manner  of  expressing, 
§81,  P7. 

Snow  load  on  roof  trusses,  §81,  p8. 

-load  stresses  in  roof  trusses,  §81,  ppl6,  23, 
33. 

Sole  plates  for  bridges,  Specifications  for,  §74, 

p21. 

Solid  floors,  Specifications  for,  §74,  pl4. 
Spacing  of  I  beams  for  hb,  §76,  p3. 

of  I  beams  for  railroad  bridge,  §76,  pl4. 
of  plate  girders  of  railroad  bridge,  §76,  p21. 
of  roof  trusses,  §81,  p4. 
of  stringers  for  hb,  §77,  p5. 
of  stringers  for  rtb,  §79,  p3. 

Span  of  I-beam  hb,  §76,  pi. 

of  I-beam  railroad  bridge,  §76,  pl2. 
of  roof  truss,  Definition  of,  §81,  p5. 
Specifications,  Bridge,  Development  of,  §74, 
pi. 

Definition  of,  §74,  p2. 
for  bracing  of  bridges,  §74,  pp21,  41. 
for  bridge  materials,  §74,  p42. 
for  bridge  ties,  §74,  ppl3,  32. 
for  connection  angles  for  floors,  §74,  ppl4, 
45. 

for  design  of  compression  members,  §74, 
pplO,  12,  29,  35. 

for  design  of  floor  members,  §74,  pplO,  15, 
32. 

for  details  of  bearings  of  bridges,  §74,  pp20, 
40. 

for  details  of  floor  systems,  §74,  ppl3,  33. 
for  details  of  pin-connected  trusses,  §74, 
ppl8,  38. 

for  details  of  plate  girders,  §74,  ppl4,  35. 
for  details  of  riveted  trusses,  §74,  ppl'7,  37. 
for  details  of  steel  trestles,  §74,  ppl9,  39. 
for  details  of  viaducts,  §74,  ppl9,  39. 
for  end  floorbeams,  §74,  pl4. 
for  flange  rivets  in  plate  girders,  §74,  ppl5, 
36. 

for  flanges  of  plate  girders,  §74,  ppl5,  36. 
for  flooring  of  deck  bridges,  §74,  pl4. 
for  guard  timbers  for  bridges,  §74,  ppl3,  32. 
for  lattice  bars,  §74,  ppl2,  31. 
for  live  load  on  bridges,  §74,  pp7,  24. 
for  longitudinal  force  on  bridges,  §74,  pp8, 
27. 

for  painting  of  bridges,  §74,  p51. 

for  piers  and  abutments,  §82,  p64. 

for  rivet  grip,  §74,  pl2. 

for  rivet  spacing,  §74,  ppl2,  31. 

for  size  of  rivets,  §74,  ppll,  31. 

for  solid  floors,  §74,  pl4. 

for  steel  castings,  §74,  p43. 

for  stiffeners  of  plate  girders,  §74,  ppl4,  35. 

for  the  construction  of  bridges,  §74,  p42. 


Specifications-— (Continued) 

for  the  design  of  railroad  bridges,  §74,  p5. 
for  the  design  of  steel  bridges,  §74,  p3. 
for  tie-plates,  §74,  ppl2,  §1. 
for  web  splices  for  plate  gilders,  §74,  ppl5, 
35. 

for  wind  pressure  on  bridges,  §74,  ppl8,  27. 
for  working  stresses  on  bridges,  §74,  pp8, 
28. 

relating  to  bearing  values  of  rivets,  §74, 
ppll,  30, 

relating  to  bolts,  §74,  p48. 
relating  to  bridge  data,  §74,  pplO,  29. 
relating  to  bridge  details,  §74,  ppll,  30. 
relating  to  bridge  inspection,  §74.  p53. 
relating  to  bridge  loads,  §74,  pp7,  24. 
relating  to  camber,  §74,  ppl3,  32. 
relating  to  centrifugal  force  on  bridges, 
§74,  pp8,  27. 

relating  to  clearance  in  through  bridges, 
§74,  p6 

relating  to  combined  stresses,  §74,  ppll, 
30. 

relating  to  connections  of  I  beams,  §74, 
pl3. 

relating  to  depth  of  bridges,  §74,  pp5,  23. 
relating  to  erection  of  bridges,  §74,  p52. 
relating  to  expansion  of  bridges,  §74, 
ppl3,  32. 

relating  to  floor  connections,  §74,  ppl3,  34. 
relating  to  gauge  of  tracks,  §74,  p6. 
relating  to  impact,  §74,  pp7,  26. 
relating  to  kinds  of  bridges,  §74,  pp5,  22. 
relating  to  mill  tests,  §74,  p44. 
relating  to  minimum  of  thickness  of 
material,  ppll,  30. 
relating  to  number  of  trusses,  §74,  p6. 
relating  to  reversal  of  stress,  §74,  ppll,  30. 
relating  to  riveting  of  girders,  §74,  pl7. 
relating  to  single-angle  members,  §74, 
ppll,  31. 

relating  to  spacing  of  deck  girders,  §74, 
pp5,  23. 

relating  to  spacing  of  stringers,  §74,  pp5, 
23. 

relating  to  spacing  of  tracks,  §74,  pp6,  23. 
relating  to  spacing  of  trusses,  §74,  pp6,  23. 
relating  to  use  of  half-through  bridges, 
§74,  p6. 

relating  to  vibration,  §74,  pp7,  26. 
relating  to  workmanship  of  bridges,  §74 
p46. 

Splice  plates,  Definition  of,  §75,  p20. 

Splices,  Flange  angle,  §75,  p23. 

Flange,  for  plate  girders,  Specifications 
for,  §74,  ppl6,  37. 

Flange  plate,  §75,  p26. 


INDEX 


xix 


Splices — (Continued) 

for  plate-girder  railroad  bridge,  §76,  p39. 
for  plate  girders,  Design  of,  §75,  pl9. 
for  wooden-bridge  members,  §80,  p28. 
in  chords  of  Towne  lattice  truss,  §80,  p34. 
in  top  chord  of  hb,  §78,  pl4. 
in  vertical  flange  plates,  §75,  p28. 

Web,  for  plate  girders,  §75,  p20. 

Web,  for  plate  girders,  Specifications  for, 
§74,  ppl5,  35.. 

Spruce,  Working  stresses  in,  §80,  p4. 
Stability  of  abutments,  §82,  p62. 

of  piers  against  overturning,  §82,  p36. 
of  piers,  Theory  of,  §82,  p23. 

Standard  structural  shapes,  §83,  pi. 

Steel  castings,  Specifications  relating  to.  §74, 
pp43,  50. 

Rivet  Specifications  for,  §74,  p42. 
roof  trusses,  Joints  for.  §81,  p49. 
Structural,  Specifications  for,  §74,  p42. 
trestles,  Specifications  for  details  of,  §74, 
ppl9,  39. 

Use  of,  in  combination  bridges,  §80,  p6. 
Stem  of  a  T  abutment,  Definition  of,  §82, 
p48. 

Sticks  in  wooden  bridges,  §80,  p24. 

Stiffeners,  Crimped,  §75,  p32. 

for  plate-girder  railroad  bridge,  §76,  p29, 
40. 

for  plate-girder  webs,  §75,  pl3. 
in  plate  girders,  End,  §75,  p31. 

Number  of  rivets  in,  §75,  p32. 
of  plate  girders,  Specifications  for,  §74, 
ppl4, 35. 

Specifications  relating  to,  §74,  p48. 

Stone  for  piers  and  abutments,  §82,  p62. 

masonry,  Joints  in,  §82,  p64. 

Straight-wing  abutment,  Definition  of,  §82, 
p53. 

-wing  abutments  Design  of,  §82,  p57. 
Streams,  Piers  for,  §82,  p20. 

Streets,  Piers  in,  §82,  pl4. 

Stress,  Reversal  of,  Specifications  relating  to, 
§74,  ppll,  30. 

sheets  furnished  to  bidders,  §74,  p4. 
Stresses,  Combined,  Specifications  relating  to, 
§74,  ppll,  30. 

Dead-load,  in  roof  trusses,  §81,  ppl6,  23, 
33. 

due  to  impact  and  vibration,  §74,  p63. 
in  beams,  §75,  pi. 

in  end  post  of  hb,  Effect  of  wind  on,  §77, 
p51. 

in  hb  lateral  system,  §77,  p42. 
in  kingrod  and  kingpost  trusses,  §80,  p9. 
in  lateral  system  ot  rtb,  §79,  p38. 
in  main  members  of  hb,  §77,  p26. 


Stresses — (Continued) 

in  main  members  of  rtb,  §79,  p21. 
in  plate  girders  of  rmlroad  bridge,  §76,  p22. 
in  portal  of  hb,  §77,  p45. 
in  portal  of  rtb,  §79,  p42. 
in  queenpost  and  queenrod  trusses,  §80, 
P17. 

in  roof  truss  with  monitor,  §81,  p30. 
in  roof  trusses,  General  methods  of  calcu¬ 
lating,  §81,  pl4. 

in  roof  trusses,  Wind-load,  §81,  ppl8,  24, 
35. 

in  wooden  bridges,  Methods  of  calculating, 
§80,  p4. 

Reversal  of,  Allowance  for,  §74,  p65. 
Snow-load,  in  roof  trasses,  §81,  ppl6,  23, 

33. 

Working,  for  roof  trusses,  §81,  p41. 
Working,  for  timber  for  wooden  bridges, 
§80,  p5 

Working,  in  bridges,  Specifications  for, 
§74,  pp8,  28. 

Stringer,  Center,  of  hb,  Connection  of,  §78,  p9. 
connections,  Specifications  for,  §74,  ppl3, 

34. 

Stringers  for  hb,  Design  of,  §77,  p4. 
for  rtb,  Design  of,  §79,  p3. 
for  rtb,  Live-load  moments  in,  §79,  p3. 
for  rtb,  Live-load  shears  in,  §79,  p3. 
for  rtb,  Spacing  of,  §79,  p3. 
of  rtb.  Bridge  seats  for,  §79,  p65. 
of  rtb,  Connection  of,  to  floorbeam,  §79,  p9. 
of  rtb,  Lateral  bracing  between,  §79,  p6. 
Roadway,  for  hb,  Connection  of,  to  floor- 
beams,  §78,  p5. 

Sidewalk,  of  hb,  Connection  of,  to  brackets, 
§78,  p3. 

Specifications  relating  to  spacing  of,  §74, 
pp5,  23. 

under  track  of  hb,  Connections  of,  §78,  p7. 
Structural  shapes,  Representation  of,  §83,  p5. 
shapes,  Standard,  §83,  pi. 
steel,  Specifications  for,  §74,  p42. 

Struts,  End,  for  rtb,  Design  of,  §79,  pl8. 
Studs  for  expansion  rollers,  §78,  p42. 
Subcontractors,  §74,  p4. 

Subfoundation  of  a  pier,  Pressure  on,  §82, 
p43. 

Substructure,  Definition  of,  §82,  p2. 
Superstructure,  Definition  of,  §82,  p2. 

System,  Floor,  for  rtb,  Design  of,  §79,  p3. 

T 

T  abutment,  Definition  of,  §82,  p48. 

abutments,  Design  of,  §82,  p52. 

Tail  of  a  T  abutment,  Definition  of,  §82,  p48. 
Tensile  working  stresses  for  timber,  §80,  p5. 


135—40 


XX 


INDEX 


Tension  members  for  pin-connected  trusses, 
Specifications  for,  §74,  ppl8,  39. 
members  of  riveted  trusses,  Specifications 
relating  to  form  of*  §74,  ppl7,  38. 
members,  Specifications  for  design  of,  §74, 
pplO,  29. 

Test,  Final,  of  a  bridge,  Specifications  rela¬ 
ting  to,  §74,  p53. 

Testing  of  mateiial  should  be  at  contractor’s 
expense,  §74,  p54. 

Tests,  Eyebar,  Specifications  for,  §74,  p45. 
of  bridge  materials,  Specifications  relating 
to,  §74,  p44. 

Thickness  of  abutment  wings,  §82,  p57. 
of  bridge  parts,  Minimum,  §74,  p30. 
of  material,  Minimum,  Specifications  for, 
§74,  ppll,  30. 

Through  bridges,  Specifications  relating  to 
clearance  in,  §74,  p6. 

Thrust,  Longitudinal,  Allowance  for,  in  rtb, 
§79,  P25. 

Longitudinal,  Effect  of,  on  piers,  §82,  p31. 

Tie-plates,  Specifications  for,  §74,  ppl2,  31. 

Ties,  on  bridges,  Specifications  for,  §74,  ppl3, 
32. 

Tight  fillers  for  plate  girders,  §75,  p33. 

Timber  for  wooden  bridges,  Kinds  of,  §80,  p4. 
for  wooden  bridges,  Working  strengths  of, 
§80,  p5. 

Use  of,  for  piers  and  .abutments,  §82,  p64. 

Time,  Extension  of,  in  bridge  contracts,  §74, 
p4. 

Top  chord  of  hb,  Splices  in,  §78,  pl4. 
chord  of  hb,  Design  of,  §77,  p39. 
chord  of  hb,  Width  of,  §78,  pl7. 
chord  of  Howe  wooden  bridge,  §80,  p26. 
chord  of  rtb,  Design  of,  §79,  p34. 
chord  of  rtb,  Eccentricity  of,  §79  p37. 
chord  of  rtb,  Splicing  of,  §79,  p48. 
course  of  a  pier,  Definition  of,  §82,  p2. 

Towers  for  viaducts,  Specifications  for,  §74, 
ppl9,  39. 

Towne  lattice  truss,  Connections  in,  §80,  p32. 
lattice  truss,  Description  of,  §80,  p32. 
lattice  truss,  Floorbeams  for,  §80,  p32. 
lattice  truss,  Lateral  system  for,  §80,  p35. 
lattice  truss,  Roof  for,  §80,  p35. 
lattice  truss,  Splices  in  chord  members  of, 
§80,  P34. 

Tracks,  Piers  near,  §82,  pl6. 

Specifications  relating  to  gauge  of,  §74,  p6.' 
Specifications  relating  to  spacing  of,  §74, 
pp6,  23. 

Transverse  bracing  of  bridges,  Specifications 
for,  §74,  pp21 , 41. 

frame  of  bh,  Connection  of,  to  truss,  §78, 
p43. 


T  ransverse — (Continued) 

frames  for  hb,  Design  of,  §77,  p45. 
frames  for  rtb,  Arrangement  of,  §79,  p41. 
working  stresses  for  timber,  §80,  p5. 

Trestle  bents,  Steel,  Specifications  for,  §74, 
ppl9,  39. 

Trestles,  Pedestals  for,  §82,  pl7. 

Pedestals  for,  Construction  of,  §82,  p66. 
Piers  for,  §82,  pl6. 

Piers  for,  Construction  of,  §82,  p66. 

Steel,  Specifications  for,  §74,  ppl9,  39. 
Truss,  Connection  of,  to  intermediate  floor- 
beams  in  rtb,  §79,  pl5. 

Kingpost,  Description  of,  §80,  p7. 

Kingrod,  Description  of,  §80,  p8. 
of  hb,  Connection  of,  to  end  floorbeam, 
§78,  P12. 

of  hb,  Connection  of,  to  intermediate  floor- 
beam,  §78,  p9. 

of  hb,  Connection  of,  to  sidewalk  bracket, 
§78,  p9. 

of  hb,  Connection  of,  to  transverse  frame, 
§78,  p43. 

Queenpost,  Description  of,  §80,  pl4. 
Queenrod,  Description  of,  §80,  pl4. 
Trusses  of  rtb,  Design  of,  §79,  p21. 

Pin-connected,  Specifications  for  details  of, 
§74,  ppl8,  38. 

Riveted,  Specifications  for  details  of,  §74, 
ppl7,  38. 

Roof,  Distance  between,. §81,  p4. 
Specifications  relating  to  number  of,  §74, 

p6. 

Specifications  relating  to  spacing  of,  §74, 
pp6,  23. 

TJ 

U  abutment.  Definition  of,  §82,  p48. 

abutments,  Design  of,  §82,  p53. 
Undermining  of  piers  and  abutments,  §82, 

p66. 

Upper  lateral  truss  of  hb,  Connections  of,  §78. 
p43. 

lateral  truss  of  hb,  Design  of,  §77,  pp43,  48. 
lateral  truss  of  rtb,  Design  of,  §79,  p44. 
lateral  truss  of  rtb,  Stresses  in,  §79,  p38. 

V 

Vertical  flange  plates,  Plate  girders  with,  §75, 
pl8. 

flange  plates,  Splices  in,  §75,  p28. 

Hip,  Drawing  of,  §83,  p27. 

Hip,  of  hb,  Design  of,  §77,  p37. 

Hip,  of  rtb,  Design  of,  §79,  p33. 
web  members  of  hb,  Design  of,  §77,  p36. 
Verticals,  Compression,  of  rtb,  Design  of,  §79, 
p31. 

Drawing  of,  §83,  p20. 


INDEX 


xxi 


Verticals — (Continued) 
of  hb,  Width  of,  §77,  p38. 

Viaducts,  Specifications  for  details  of,  §74, 
ppl9,  39. 

Vibration,  Effect  of,  on  bridge  stresses,  §74, 
p63. 

Views,  Shortened,  of  bridge  parts,  §83,  p3. 

W 

Web,  Effect  of,  in  resisting  bending  moment, 
§75,  p6. 

Floorbeam,  for  hb,  Design  of,  §77,  ppl8, 
24. 

members  of  hb,  Design  of,  §77,  p35. 
members  of  riveted  trusses,  Specifications 
for,  §74,  ppl7,  18,  37,  38. 
members  of  rtb,  Design  of,  §79,  pp30,  31, 
33. 

of  intermediate  floorbeams  of  rtb,  Design 
of,  §79,  P12. 

of  plate  girder,  Design  of,  §75,  plO 
of  stringers  of  rtb,  Design  of,  §79,  p5. 
Plate-girder,  for  railroad  bridge,  Design  of, 
§76,  p28. 

Plate-girder,  Resisting  moment  of,  §75,  p20. 
Plate-girder,  Shear  in,  §75,  pl2. 
plates,  Specifications  relating  to,  §74,  p48. 
-splice  rivets,  Resisting  moment  of,  §75, 

p21. 

splices  for  plate  girders,  Design  of,  §75,  p20. 
splices  for  plate  girders,  Specifications  for, 
§74,  ppl5,  35. 

Weight  of  hb,  §77,  p30. 
of  rtb,  §79,  p23. 

Weights  of  bridges,  §74,  p66. 

Welding,  Specifications  relating  to,  §74 
p46. 

Wheel  guards  for  wooden  floors,  Specifica¬ 
tions  for,  §74,  p34. 

White  oak.  Working  stresses  in,  §80,  p4. 
pine,  Working  stresses  in,  §80,  p4. 

Width  of  a  bridge,  §74,  p57. 
of  base  of  abutment,  §82,  p51. 
of  hb,  §77,  p3. 
of  rtb,  §79,  p3. 
of  top  chord  of  hb,  §78,  pl7. 
of  verticals  of  hb,  §77,  p38. 

Wind  load,  Allowance  for,  in  stringers  of  rtb, 
§79,  p5. 

load  on  hb,  §77,  pp31,  42. 
load  on  I-beam  railroad  bridge,  §76,  pl5. 
load  on  plate-girder  railroad  bridge,  §76, 
p25. 

-load  stresses  in  roof  trusses,  §81,  ppl8,  24, 
35.  . 

pressure,  Allowance  for,  in  intermediate 
floorbeams  of  rtb,  §79,  pll. 


Wind — (Continued) 

pressure,  Allowance  for,  in  stringers  of  rtb, 
§79,  p5. 

pressure,  Allowance  for,  in  trusses  of  rtb, 
§79,  p24. 

pressure  on  bridges,  Specifications  for,  §74; 
PP8,  27. 

pressure  on  hb,  §77,  p31. 
pressure  on  piers,  §82,  p27. 
pressure  on  pieis,  Overturning  moments 
of,  §82,  p33. 

pressure  on  plate -girder  railroad  bridge, 
§76,  p25. 

pressure  on  roof  trusses,  §81,  p9. 
pressure  on  itb.  §79,  p38. 
stresses,  Effect  of,  on  end  post  of  hb,  §77, 
p51. 

stresses  in  hb  lateral  system,  §77,  p42. 
Wing  abutment,  Definition  of,  §82,  pp2,  48. 

abutments,  Types  of,  §82,  p53. 

Wings,  Abutment,  Forms  of,  §82,  p56. 
Abutment,  Size  of,  §82,  p56. 

Abutment,  Thickness  of,  §82,  p57. 

Pier,  Definition  of,  §82.  p2. 

Wood,  Use  of,  for  bridge  construction,  §80, 
pl 

Wooden  bridge,  Howe,  Chords  of,  §80,  p26. 
bridge,  Howe,  Lateral  system  for,  §80,p31. 
bridge,  Towne  lattice  (see  Towne). 
bridges,  General  methods  of  calculating 
stresses  in,  §80,  p4. 
bridges,  Kinds  of  timber  for,  §80,  p4. 
bridges,  Types  of,  §80,  p3. 
bridges,  Uses  of,  §80,  pl. 
floors  for  bridges,  Specifications  for,  §74 
p32. 

Howe  truss,  Description  of,  §80,  p24  . 
roof  trusses,  Joints  for,  §81,  p44. 

Work,  Extra,  Specifications  relating  to,  §74, 
p53. 

Working  drawings  submitted  by  contractor, 
§74,  P4. 

lines  of  I-beam  railroad  bridge,  §76,  pl8. 
strengths  of  timber  for  wooden  bridges,  §80, 
p5. 

stresses  for  roof  trusses,  §81,  p41. 
stresses  in  bridges,  Specifications  for,  §74, 

pp8,  28. 

stresses  in  I-beam  hb,  §76,  p9. 
Workmanship  of  bridges,  Specifications  rela¬ 
ting  to,  §74,  p46. 

Wrought  iron,  Specifications  for,  §74,  p43. 
iron.  Use  of,  in  combination  bridges,  §80, 

p6. 

Y 

Yellow  pine,  Working  stresses  in,  §80,  p4. 


